Here's an idea that's been rotating in my brain for a few days: Bowser on a leash.
Somebody's threatening the world again, and to get Bowser out of the way they capture him and chain him up, making him walk on a leash whenever they have to change locations. Bowser's furious of course, but he doesn't get a chance to break free before Mario and Co. show up and beat the boss that was left in charge of him.
Mario and Luigi are just barely too nice to make fun of him to his face (though it's a struggle), and set him free. Oddly, the leash doesn't want to come off. It must be magic. Bowser says he'll accompany them because he wants to utterly destroy the people responsible for humiliating him like this, but when the Mario party starts to leave Bowser doesn't follow.
After a minute they realize he can't. The leash is enchanted so that Bowser cannot move his legs unless someone is holding it.
Bowser refuses to let Mario be the one to hold it (if Peach is in the party she'd refuse because it's just too weird, and if there are any Toads they'd be too scared) so that leaves Luigi. He tries to make the best of it but Bowser isn't helping. He makes demands, he acts out, he won't cooperate. If Luigi asks him to do something he'll either ignore it or do it in the least efficient way possible.
It goes on like this for days, and it's also not helping that Bowser refuses to be seen in this situation so he won't go in to any towns. He and Luigi have to take the long way around while the others get to shop and rest and get information from locals.
It's on one of these side trips that Luigi finally snaps and says something about Bowser's behavior, and Bowser immediately turns on him and yells that Luigi has NO idea how it feels being stuck like this. How demeaning it is, how Bowser can't forget it even for a moment.
"I have to ask you permission to do anything!"
"You don't have to ASK, you can just tell me! I won't say no."
And Luigi notices that Bowser seems... not so much upset as... disappointed? Almost like he wanted Luigi to refuse him?
Like maybe all his uncooperative behavior the last few days was intentional and he's been waiting to be punished.
Oh. Oooooh. Okay Luigi didn't see this coming. And since Bowser actually doesn't seem like he understands why he's feeling this way, it would be wrong to take advantage of it.
So instead of punishing him for acting out, Luigi will praise him when he helps! A perfect plan!
Bowser's ego is huge but it's also fragile, and it doesn't take long before he's eager to get any sort of kind word from Luigi. By the time the rest of the party join them, only a day later, Luigi has Bowser (metaphorically but Bowser would definitely do it literally if properly incentivized) eating out of the palm his hand.
Too bad Luigi hasn't thought through what to do once they do find someone who can get the leash off. Making a guy with infamous attachment issues emotionally dependent on you miiiiiight backfire a little bit.