I want to try to make a case for shove as a bonus action, knowing I'm probably wrong and I can already imagine the (valid) responses to the arguments I'm going to make, but I *like* shove as a bonus action, so I want to try to make that case.
I haven't played tabletop D&D since... I think 1999? (which by the way has a cool story of IRL border guards taking the copy of Thieves Handbook that was sitting on the dashboard for a look-through before letting us cross!). So 5e rules are super new to me. I never had any reason to doubt shove was a reasonable bonus action until I saw people disagreeing with that here.
I thought about it. You're right. It should be a full action. I've never been in a sword fight that wasn't sporting in nature, where nobody gets shoved, so I don't know. I tried imagining shoving someone in combat, and maybe a two handed shove off a ledge is a full action, but stupidly trying to push them after taking swing is a bonus action? That's too convoluted for game rules, it has to be one or the other.
So while I agree it should be a full action, drinking a potion is a bonus action. Really? Do I have tactical belt of potions with quick-release tops? How in the world is *that* a bonus action? It is because it's a convenience to keep things fun by not getting your ass kicked too much.
Switching weapon sets isn't a thing at all. You can spend half your turn swapping weapon sets, and that's fine. Why isn't that an action? I think for the obvious reason that it's easy as hell to fat-finger the swap weapon sets key, and it would be really, really lousy to get your ass kicked on account of that. It makes sense as part of the game.
And I would argue the same applies to shove. Should it be a full action? Yeah, I'll admit that. But having it as a bonus action keeps the game fun. You can shove an enemy and run up stairs away from them, make a ranged attack, and force them to use dash on their next turn. This makes otherwise impossible encounters possible.
The obvious argument against that is that impossible encounters shouldn't be possible. I disagree. This is a game, not really life. Real life sucks most of the time, and we play a game because it's fun, the world makes sense, and the rules are finite and clear. If you don't like it as a bonus action, don't use it that way.
We don't have difficulty levels yet, and I while I think it's extraordinarily unlikely something like making shove a bonus action or action based on (eventual) difficulty setting would happen, you'll almost certainly have the opportunity to crank up the difficulty to compensate.
So yes, it should be a full action, but the game is more enjoyable because it isn't.
