Bowser's well designed for casual free for alls, so I find him to be better suited to doubles than other heavies like DK and Charizard. I don't play competitive doubles, but when I do it casually, my typical partner runs Bowser Jr for our Father Son Bonding Exercise. It's not a very effective team, but it's taught me how well Bowser can work in tandem with a partner. Maintaining a frontline for Jr to charge up a 20% damage cannon behind you (and of course dodging it if you're still in its flight path). Coming down on people with aerial Fire Breath in time with Jr's Clown Kart advance. Timing a Bomb to land on whoever steps up to block an incoming Mechakoopa.
ZSS seems to be the ideal partner. She's swift and has the air statistics and flip kick to move over and around Bowser's mighty moveset, especially if he keeps to the ground. Bowser lands a stray hit from the ground that knocks the target in the air, and there she is, chaining Uairs into an Up B. Her Bury and Stun attacks lend Bowser some extremely powerful punishes, more powerful moves than she could ever land on her own. If Bowser catches an opponent in Fire Breath and ZSS is right behind, she can flip kick over for some serious damage. It's a little ironic that our worst matchup in Singles happens to be the best partner in Doubles. Strange bedfellows and all that.
There are a lot of doubles partners that I don't think Bowser syncs with. Namely the long range zoners such as the links and Villager. You might think an aggressor paired with a zoner makes for a balanced team, but both are crippled when working together. Bowser wants to take the frontline, and they can't shoot past his large frame. So Bowser's only option is to put himself between his two opponents. And Bowser is garbage when surrounded. Maybe Robin could show promise as a partner. I just really really want to be the guy who follows up from that arcthunder.