Dumping Con is not a good idea... (+ suggested "build")
I'll address your whole concept in this answer, but Bottom Line Up Front is that your PC is a spell caster. The linkage between concentration and Constitution impacts play, and, low Dexterity reduces Armor Class so you'll get hit a lot more often, triggering Concentration / Constitution saves. You need some HP to absorb some of that and you need some workarounds (addressed later).
Dumping Dexterity is needlessly penal to your PC
Choosing a dexterity score with negative stat modifiers (9 (-1)) means that your Initiative roll will more often place you later in the initiative order during combat — this can reduce the effectiveness (1) of your buffing your allies with Bardic Inspiration and (2) of getting your buff / debuff spells up and running. Your PC intends to "stay out of the way" to mitigate low armor class, but there are some other ways to avoid hits and enemies may target you anyway with ranged attacks, or by swarming the party. (More at the end / workarounds).
A slightly better approach / build based on how Constitution impacts you as a spell caster in this edition of the game.
- Dropping the INT to 14 still achieve your skill / concept aims along with your 14 WIS.
- A key bard feature is that you can use Bardic Inspiration for an ally's crucial skill check (and yourself at level 14 if your game gets that far).
- The fact that, being a gnome, you have advantage on all INT, CHA, and WIS saves will pay off in later levels as more INT and CHA saves crop up — it helps all game long for WIS saves (which are fairly common).
Some "tricks and tips" for this edition
The three most common saving throws are Dexterity, Wisdom, Constitution. Since you are proficient in Dexterity saving throws as a Bard, you won't feel it quite as hard as classes that are not proficient in the Dex Save. You are +2 on your rolls out of the gate with a Dexterity of 10 and it increases at levels 5, 9, 13, etc.
Choose the College of Lore (skills aplenty!). Your STR and DEX do not fit College of Valor.
Proposed stat line up — STR: 8 DEX: 10 CON: 12 INT: 14 WIS: 14 CHA: 16
Per your concept, focus on the "skill master" and "support" features of the bard class. The mechanics of Proficiency and Expertise overwhelm the +1's for Ability Score increases as you go up in level — that is where you get the serious skill boosting.
- Tip/trick: remember to get "help" from other PCs (Chapter 7, Working
Together) on as many skill checks as you can in order to get
advantage on the die rolls. (Roll 2d20, pick the best roll). And
you help them also, where you can.
Working Together
Sometimes two or more characters team up to attempt a task. The character who’s leading the effort—or the one with the highest ability modifier—can make an ability check with advantage, reflecting the help provided by the other characters. (PHB Chapter 7; Basic Rules, p. 62)
That will vary somewhat with the situation, of course.
Proficiency / Expertise choices beat ASI boosts to INT
You don't need to boost INT to be effective in your chosen Skills. My suggested array to meet your concept objectives. STR: 8 DEX: 10 CON: 12 (+1) INT: 14 (+2) WIS: 14(+2) CHA*: 16 (+3)
An important thing about this character is that I want him to be knowledgable about history, arcana, religion and insight, so Intelligence is very important to me unlike most Bards.
You chose three INT based skills (History, Arcana, Religion), and one WIS based skill (Insight). I am guessing you chose a Sage, Hermit or Acolyte Background. You get 3 skills as a Bard plus 2 from your Background for a total of 5.
- I suggest Persuasion or Deception as the fifth one; your proficiency in three musical instruments should suffice for Barding It until level 3, so there is no need to pick Performance to start out based on your character's mentor theme.
Being proficient in these four desired skills boosts your chances for successful skill rolls as you level up.
Since this question tag is optimization, apply your ASIs (+2) to Charisma at level 4 and level 8 to ensure that
- your spells are their most effective (best spell save DC and bet "to hit" with cantrips/attack spells) and ...
- you increase the number of Bardic Inspiration dice uses that you get per rest. <== That's a major feature for helping your party; it fits with your "wise old helpful gnome" concept.
The difference in having a Proficiency bonus + INT bonus (2 +2 (14 INT)) and (2 +3 (16 INT)) is not significant. For a DC of 15 you'll make the roll (target number of 10 or 11) either 55% of the time or 50% of the time. For a DC of 12 70% or 65% of the time. At third level, you come into the killer bonus: Expertise. It doubles your proficiency bonus.
Which two skills do you want to really rock with?
At 3rd level, choose two of your skill proficiencies. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies. At 10th level, you can choose a other two skill proficiencies to gain this benefit. PHB, p. 54)
Illustration: (using Expertise in History and Religion)
Expertise with a 14 Int in History, Religion: +2 + 4 at level 1 = + 6
(if "just proficient) it's +4 (Insight, Arcana)
Expertise with a 14 Int in History, Religion: +2 + 6 at level 5 = +8
(If just proficiency) it's +5 (Insight, Arcana)
Expertise with a 14 Int in History/Religion: +2 +8 at level 9 = +10
(If just proficient it's +6) (Insight, Arcana)
{You get to add Expertise to two more skills at level 10}
Expertise with 14 WIS/INT for Insight/Arcana: +2 +8 at level 10 = +10
There's your skill emphasis: now for two important stats. (Con to 12 / Dex to 10)
Con: Support caster? Keep your concentration up
You will start with 9 HP with a 12 CON, and get 6 per level up. You need these HP. Enemies hit with some frequency, and some hit kinda hard.
Your Tasha's Hideous Laughter is a great spell to debuff an enemy — if you keep your concentration up. So too is Slow once you get to level 5. (If using Tasha's optional rules; otherwise, get Slow at level 6 with one of your magical secrets).
If a spell must be maintained with concentration, that fact appears in its Duration entry ... The following factors can break concentration:
- Casting another spell that requires concentration.
- Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.
- Being incapacitated or killed. You lose concentration on a spell if you are incapacitated or if you die. (Basic Rules, pages 83-84)
Getting hit while concentrating on a spell forces a Constitution saving throw. The +1 to that die roll won't hurt your chances to make that save and not lose concentration. Having a few more HP can be the difference between being knocked out, or to still be standing with your buff / debuff working for your party. If you are a back liner / support caster, your bread and butter includes a variety of concentration spells. They are only good if you keep them running.
Don't penalize your Dexterity saving throw
Dexterity saving throws are one of the most common in the game. Having a penalty for that ability-based saving throw will increase the number of times you'll be unable to support your party. There is no need to boost Dexterity if you don't want to — your character concept can work if you are wary and careful. It's still a poor idea to penalize your Dex saving throw.
And now for the "workarounds"
With the lack of armor due to low dexterity, you need to be crafty to avoid being hit; if you can avoid being noticed that's even batter.
How to reduce chances to be hit
Partial cover gives you +2 AC; three quarters cover gives you +5 AC. Find people or things to hide behind when combat comes. Full cover prevents a lot of attacks.
As soon as you can, get studded leather armor. It's only +1 to AC but you need it.
Use Cutting Words (Bard, Lore, level 3 ability) to turn a hit on you into a miss. I) to subtract 1d6, or 1d8, (whatever your Bardic Inspiration die is) from an attack roll that would hit you.
Use the Minor Illusion cantrip.
In some situations, you can create cover by placing an illusion in front of your small-sized gnome with the Minor illusion cantrip. If the illusion is between you and whomever is shooting at you, full cover (you are shorter than 5' tall, the the illusion can be 5' on a side) can keep you from being seen. For a lot of ranged attacks that means "no attack" happens. AoE attacks / spells / effects will still get to you.
- Tip/Trick: Make sure to include the Minor Illusion cantrip on your cantrip list either now, or when you get your next cantrip at the level. (I like Dancing Lights, so don't let me dissuade you from that initial choice)
If you are a Forest Gnome, you have the minor illusion cantrip as a racial feature. If you are a Rock Gnome, you won't. In my experience, that cantrip is very useful both in and out of combat.
Mirror Image: may be needed sooner than later.
Mirror Image is a second level spell. Spell choices are one of those tricky things for a bard. If you find that you get hit a lot you may need to invest in Mirror Image. It stays active without concentration, and it absorbs a few hits before the illusory gnomes dissipate under the attacks.
Invisibility — requires concentration
Sometimes, turning invisible is what you need to do, but since it requires concentration you then cannot at the same time buff your allies or debuff your enemies. Even with those shortcomings this is an effective, albeit situational, work around. Darkness has similar limitations: you can't be seen by most things, but it hampers your allies and requires concentration.
Other workarounds to deal with Con or Dex issues — feats
If your table uses feats from the PHB, there are some that can help you at level 4 or 8 if you will accept that (1) you get fewer Bardic Inspirations per rest, and (2) your spell save DC's won't be as high. I'll not take build advice beyond level 10 since most campaigns don't get that far. If yours does, and you wonder at your choices then, post a question at that time. (I will suggest that at level 12 you make sure that Charisma is maxed (20) if it has not been already).
- War Caster: You get advantage on Constitution Saving Throws to maintain concentration on a spell (roll 2d20 take the best roll) and you can use a spell to make an Opportunity Attack when that occasion arises.
- Resilient (Constitution): +1 Constitution, and proficiency in Constitution Saving Throws. (+2 at level 4, +3 at level 5, etc ...)
- Alert: you are never surprised, and you get +5 to Initiative. Other creatures don’t gain advantage on attack rolls against you as a result of being unseen by you.
- A note on this feat, which I used on a sorcerer. This turned out to be surprisingly good in play. It won't increase your armor class but it prevents some attacks from having advantage on you. The boost to initiative helps you to go first more often to buff, debuff, inspire, flee, whatever. The other PCs got the benefit of my buff spells sooner, more often. We were, as a group, pleasantly surprised with the resulting benefit for the team — well, except for me, who was never surprised. ;-)
- Tough: more HP
- Mobile: When you make a melee attack against a creature, you don’t provoke opportunity attacks from that creature for the rest of the turn, whether you hit or not. (Also, fastest gnome in the west) You swing, you miss, you move away. No OA against you. (Most of the other feats are better)
- Lucky: advantage on a save (or attack roll, or a skill check) three times per day. This feat is one of the best in the game, and will address a couple of your core weak areas: Constitution Saves, and Dexterity Saves.
- Moderately Armored. This lets you wear medium armor, and use a shield: chain shirts, breast plates, half plate. This may mitigate some of the armor class problems from low dexterity. How that meshes with your low strength (the feat adds 1 to STR or DEX) will need to be squared with whatever encumbrance rules your table is using. If your character scheme eventually arrives at "OK, I'll wear armor and a shield" then a breastplate and shield kit boosts AC to 16.
Are there ways I can use INT to my advantage as a bard?
As you can see from T.J.L's answer, and mine, proficiency and expertise will help you with a lot of the skill checks as you go up in level, so you could adjust your build to STR: 8 DEX: 10 CON: 14 INT: 12 WIS: 14 CHA: 16. That's what I would do, but your theme will work as is.
How you can get more out of your INT as a bard is to keep taking more INT based skills.
You will start with Religion, History, Arcana, Insight and one more. You get three more at level 3. Add Investigation and Nature to your skill base at level three and you have all 5 of the INT proficiencies.
Bonus Proficiencies
When you join the College of Lore at 3rd level, you gain proficiency with three skills of your choice. (SRD, p. 13)
Your proficiency boosts and your INT modifier will make you more likely to pass these skill checks and it fits your theme.
That leaves another one for Performance, Perception, Survival or whatever suits your fancy.
Another way to use your INT score to your advantage is to, at some point, multiclass into Wizard to get four utility spells and a spell book.