You all meet in a bar

You're the GM and you have a bunch of PCs with non-intersecting backstories first meet each other in a public place.

What do you do to make it so they would "party up" so to speak and go around doing stuff together?

The classic choice is the quest, offer them a lucrative job which will require them to work together, then just hope your players aren't non-roleplaying morons.

Not all characters will accept random job offers, especially dangerous ones. And of course players will take any excuse to hang out in-character but a better GM can tie it all in.

OP what about they all get kidnapped and as they escape whatever prison they're in, they befriend eachother and vow to get to the bottom of the mystery. Or something. Might be too rail-roady.

>Not all characters will accept random job offers, especially dangerous ones

It's at least partially the player's job to get their character interested in the story. Nobody enjoys a game grinding to a halt while the DM tries to work what the fuck is going to make John's monk stop talking about how all physical reward is ephemeral and accept the damn job so we can play.

Read Foodfight (Shadowrun module).

>And of course players will take any excuse to hang out in-character but a better GM can tie it all in.

Someone throws another man on the table the PCs are eating at. Their meal is ruined, their drinks spilled and their clothes completely fucked.

Turns out the guy that threw that man is a big, hulking thug belonging to a biker gang, who is now laughing at the PCs for how stupid they look with pasta, ravioli and beer all over them. They think it's really, really funny.

What do you do?

Give them a common enemy

...

To be honest, the best way to solve this problem is just to circumvent it. I find its usually a much better start to give (or, prefferably, invent with your players) a starting scenario which roughly defines their relationships e.g. "You are a band of mercenaries, and have just recieved a strange letter..." Its best to do this before characters get put together, for obvious reasons.

It means you don't have to faff around with taverns as the PCs now have at least a rudimentary link to each other, and that you can immediately throw a couple of appropriate hooks or encounters their way to get the ball rolling. If you can pull it off, you can even start them already on some kind of job.