Your players are rejecting already balanced options - feats, multiclassing, spells, items, etc - but asking for a free option that does the same thing.
For something to be balanced there needs to be a give and take. In this situation players have no reliable bonus action so the bonus action cost isn't truly a cost. Similarly, if they are 5ft away then a bonus action dash is superior to an action dash. This means it will be inherently unbalanced, even if you only let them move 5ft.
There are a lot of options for your players already in the game, I would encourage them to pick one of those as they are already balanced. Here is a (non-exhaustive) list of bonus actions I saw on Reddit:
Enter or end Rage - Barbarian level 1 Rage feature.
Make a melee weapon attack while raging - Barbarian/Path of the
Berserker level 3 Frenzy feature.
Dash - Barbarian/Path of the Totem Warrior level 3 Eagle Totem Spirit
Knock a Large or smaller creature prone when you hit it in melee -
Barbarian/Path of the Totem Warrior level 14 Wolf Totemic Attunement
Give Bardic Inspiration to a creature - Bard level 1 Bardic
Make a weapon attack if you use your action to cast a Bard spell -
Bard/College of Valor level 14 Battle Magic feature.
Command creatures charmed by your Charm Animals and Plants feature -
Cleric/Nature level 17 Master of Nature feature.
Move your illusion - Cleric/Trickery level 2 Invoke Duplicity feature
Move all of your illusions - Cleric/Trickery level 17 Improved
Make one weapon attack when you take the Attack action - Cleric/War
level 1 War Priest feature.
Revert to your normal form - Druid level 2 Wild Shape feature.
Use Wild Shape - Druid/Circle of the Moon level 2 Combat Wild Shape
Regain HP by expending a spell slot while transformed - Druid/Circle
of the Moon level 2 Combat Wild Shape feature.
Second Wind - regain 1d10+CL HP - Fighter level 1 feature.
Commander’s Strike - give a friend a free attack as a reaction -
Fighter/Battle Master maneuver.
Feinting Attack - get advantage on the next attack roll -
Fighter/Battle Master maneuver.
Rally - add temporary HP to a friend - Fighter/Battle Master maneuver.
Summon a bonded weapon - Fighter/Eldritch Knight level 3 Weapon Bond
Weapon attack when you cast a cantrip as your action -
Fighter/Eldritch Knight level 7 War Magic feature
Weapon attack when you cast a spell as your action - Fighter/Eldritch
Knight level 18 Improved War Magic feature
Unarmed Strike when you use the Attack action with an unarmed strike
or monk weapon - Monk level 1 Martial Arts feature.
Flurry of Blows, Dodge, Disengage, Dash - Monk level 2 Ki feature.
Teleport up to 60ft - Monk/Way of Shadow level 6 Shadow Step feature.
Water Whip - Monk/Way of the Four Elements discipline.
Cast a Paladin spell with a casting time of 1 action - Paladin/Oath of
the Ancients level 20 Elder Champion feature.
Vow of Enmity - advantage on attack rolls against one creature -
Paladin/Oath of Vengeance level 3 Channel Divinity feature.
Hide - as the action - Ranger level 14 Vanish feature.
Command your companion to Dash, Disengage, Dodge, or Help -
Ranger/Beast Master level 7 Exceptional Training feature.
Dash, Disengage, Hide - as the same action - Rogue level 2 Cuning
Dexterity (Sleight of Hand) check, use thieves' tools to disarm a trap
or open a lock, Use an Object - Rogue/Thief level 3 Fast Hands
Control a Mage Hand created by the cantrip - Rogue/Arcane Trickster
level 3 Mage Hand Legerdemain feature.
Distract a target with your Mage Hand - gives you advantage on attack
rolls - Rogue/Arcane Trickster level 13 Versatile Trickster feature.
Convert between spell slots and sorcery points - Sorcerer level 2
Flexible Casting feature.
Cast a spell with casting time of 1 action - Sorcerer Quickened Spell
Create or dismiss dragon wings - Sorcerer/Draconic Bloodline level 14
Dragon Wings feature.
Teleport up to 20ft - Wild Magic Surge effect.
Make an illusory object real - Wizard/Illusion level 14 Illusory
Make a weapon attack or shove a creature when you use the Dash action
Attack with a hand crossbow when you attack with a one-handed weapon -
Crossbow Master feat.
Make a melee weapon attack when you crit or reduce a creature to 0 -
Great Weapon Master feat.
Melee weapon attack with the opposite end of a weapon - Polearm Master
Attempt a grapple when you hit with unarmed strike or improvised
weapon - Tavern Brawler feat.
Spells with a casting time of a bonus action
Banishing Smite, Blinding Smite, Branding Smite, Compelled Duel,
Divine Favor, Divine Word, Ensnaring Strike, Expeditious Retreat,
Flame Blade, Grasping Vine, Hail of Thorns, Healing Word, Hex,
Hunter's Mark, Lightning Arrow, Magic Weapon, Mass Healing Word, Misty
Step, Sanctuary, Searing Smite, Shield of Faith, Shillelagh, Spiritual
Weapon, Staggering Smite, Swift Quiver, Thunderous Smite, Wrathful
Spells which allow you to do something as a bonus action
Animate Dead, Animate Objects, Create Undead, Dancing Lights, Flaming
Sphere, Grasping Vine, Mordenkainen’s Sword, Spiritual Weapon, Unseen
Servant - command summoned creatures or objects.
Arcane Gate - rotate the gate.
Aura of Vitality - heal one creature in range for 2d6 HP.
Bigby's Hand - move the hand or crush a grappled creature.
Compulsion - command targets to move in a direction of your choice.
Expeditious Retreat - Dash, as the action.
Flame Blade - resummon the blade if you dropped it.
Gust of Wind - change direction of the wind.
Heat Metal - cause the spell's damage again.
Hex - move the curse on another creature, if the cursed creature died.
Hunter's Mark - move the mark on another creature, if the marked
Mislead - switch between using your senses or those of your illusion.
Swift Quiver - make two attacks which use ammunition.
Attack with an off-hand weapon - Two-weapon fighting.
take two levels of rogue to gain cunning action.
take the scout subclass in rogue, so that you can spend a reaction to
move half your speed if a creature ends its turn within 5ft if you.
Use the expeditious retreat spell-it’s a concentration effect, but it
allows you to take the dash action as a bonus action.
take 2 levels in monk so you can spend ki points to dash as a bonus
if you’re talking about the latter, that’s generally harder to do, but
Play a monk-their movement speed increases with character level.
Play a wood elf-they get a 5ft bonus to move speed (or a half elf with
wood elf ancestry from SCAG).
Take the squat nimbleness racial feat in xanathar’s-it gives a +5ft
bonus to speed.
Take the mobile feat-it offers a +10ft bonus.
Use the Longstrider spell-it also offers a +10ft bonus.
Use a mount-their move speeds and move modes replace yours.
Wild elf gets a bump
Monk class, and barbarian classes get a bump
2nd level rogue gets a move as a bonus action
Ranger, hunter enclave, gets it later on
Athletic feat gives you an effective climb speed
Various spells, long strider, expeditious retreat, teleportation magic
There are a lot of options that are completely within your players' power to explore. Encouage them to use their agency to solve their own problems rather than asking the DM to give them something for free.
If you do want to make this even knowing it's unbalaned and knowing your players already had ample choice to get themselves a BA, make it as weak as possible. 5ft is the practical limit. Again, I don't think it's a good idea, but that will have the least balance implications.