You can try, and perhaps succeed (easier with two PCs)
You have the set up for a great idea for dispatching a human sized foe. Or maybe, you want to give them a vacation on the astral plane and they aren't very keen on the idea.
- Artificer of level 7 can have more than two infused items, and bag
of holding is makeable at level 2.
- You have two bags of holding. (I'll get to "why two?" later)
Shoving (work a little with your DM on this part)
Strictly speaking, the rules are silent on a targeted shove, but there's no reason that you can't try to target a shove. Shove and/or grapple is an ability check; it will be an opposed ability check per Chapter 7 and/or Chapter 9.
[...] you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them. A Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). You succeed automatically if the target is incapacitated. If you succeed, you subject the target to the grappled condition.
Moving a Grappled Creature. When you move, you can drag or carry the
grappled creature with you, but your speed is halved, unless the
creature is two or more sizes smaller than you.
Shoving a Creature
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
Your PC can move them once you grapple them, but it's still tricky to stuff them into that hole; I think calling for a shove is a good application of that rule, or, the DM could call for a general Strength check per Chapter 7.
What else you need: two ten foot poles, tied together.
Or two spears, two lances, something that is more than 10' long. Let's say that we want 14' of reach to stay outside of the 10' blast radius of the astral plane entry event.
Aside: if two members of your party can cast Mage Hand, on mage hand can be used to hold the empty bag open while the other mage hand can put the full bag into the empty bag, and keep all of you outside the 10' danger radius.
This ability check may be made with disadvantage
Or not. That's up to your DM.
The DM can also decide that circumstances influence a roll in one
direction or the other and grant advantage or impose disadvantage as a
result. (PHB, Chapter 7, Using Ability Scores)
And here's how it works.
By yourself ....
a. You can hold the bag of holding, make a Grapple (and then if you succeed) make a Shove attempt. You are trying to shove them into the bag; since shoving isn't necessarily targeted, you may get disadvantage on this attempt.
Were I DM, I might lay disadvantage on this attempt, and I might not. If the target were a gnome, I'd not lay on disadvantage. You can also apply the 'Shove Aside' optional rule (DMG, p. 252). This lets you make a shove attack to move a creature in an arbitrary direction, but you do so with disadvantage. (thanks to @BBeast for suggesting a reference to that).
With two successes in a row, into the bag they go. If you do not have additional attacks, for example a rogue or an artificer, then it takes two turns to do this and there may be an additional chance to fail as the grappled creature tries to escape the grapple.
We are pretty sure that the bag of holding can't be opened from the inside
b. Open the second (empty) bag of holding, and then carefully drape the (full) bag containing the bagged creature over the end of the pole mentioned above. Make sure you are more than 10' away from the empty bag. Carefully lift the pole and place the full bag into the empty bag.
Placing a bag of holding inside an extradimensional space created by
a Heward’s handy haversack, portable hole, or similar item instantly
destroys both items and opens a gate to the Astral Plane. The gate
originates where the one item was placed inside the other. Any
creature within 10 feet of the gate is sucked through it to a random
location on the Astral Plane. The gate then closes. The gate is
one-way only and can’t be reopened.
The bag of holding is indeed "a similar item." They just got a one way ticket to the astral plane.
With the aid of an ally
a. Make sure that your ally uses the help action to assist you with the shove into the bag. That gives you advantage. This will either cancel the disadvantage the DM gave you, above, or it will make for a more likely success.
b. Proceed as above with the poles, and have the ally help you again. The DM may require an ability check to get the full bag into the empty bag, so having advantage on that check is a good plan.
Set yourself up for success!
Get the party's Bard to lay some bardic inspiration on you.
Get the Cleric of the Druid to cast guidance on your character;
additions to the ability check are handy here!
If there is a spell caster, enhance ability might be what you need
to get this ability check over the top and succeed.
Bull’s Strength. The target has advantage on Strength checks, and his
or her carrying capacity doubles. (PHB, Enhance Ability, Ch 11)
Better yet, incapacitate the target first ...
... and then stuff them into the bag, and then do the thing with the poles and the empty bag. An incapacitated target can easily be shoved into the bag if they fit at all.
An incapacitated creature can't take actions or reactions.
Or paralyze them... (See Appendix A, Conditions, Paralyzed) ...
... or, knock them out first
An unconscious creature is incapacitated, can't move or speak, and is
unaware of its surroundings. The creature drops whatever it's holding
and falls prone. The creature automatically fails Strength and
Dexterity saving throws. Attack rolls against the creature have
advantage. Any attack that hits the creature is a critical hit if the
attacker is within 5 feet of the creature.
You can use the knock out rule from the PHB Chapter 9, put them to sleep, or use other means to render the foe unconscious.
For further shennanigans
Craft or otherwise acquire a bag of devouring, polymorph the enemy into a small beast (snail, clam, slug, earth worm, etc) and then drop the enemy into the bag of devouring. Problem solved. (Thanks to @SumofeDpi for reminding me)