I know they had a reeeeaall rough start being on opposite sides of a coup. But listen. Bolin wants EVERYONE to like him. He learned the hard way that he had been manipulated by Kuvira and completely wrong in supporting her. I realize this doesn't mean he's immediately wanting to be Wu's best friend, but it removes the main barrier to them getting along.
Wu is also the kind of person that wants friends and wants people to like him. And there's no way he would hold a grudge against his boyfriend's brother.
I personally really like the idea that Bolin is like... A lil standoffish about Wu the first time he comes back to republic city after the invasion. He's not really like, mad at Wu or dislikes him but maybe he's still a little unsure... Is this guy really fit to be a king? how much of my opinion of him was colored by kuvira's manipulation? Is he a total snobby jerk? And then Pabu runs up to Wu and snuggles his face and licks his nose and Wu is delighted. And Bolin is like OH yeah no this guy is good. All clear. Pabu approves.
I like to think once Mako and Wu are together Bolin is excited. not just that his brother's got somebody but that his family is growing ever-larger.