I'm actually wildly optimistic about Bowser's chances with Rosalina. The new Uthrow collateral hit will delete Luma off the stage very commonly on small stages like Battlefield, or on platforms. Even if it's not killed, it's hit far enough away that Luma shouldn't be able to interrupt Uthrow followups. Fire Breath desyncs Luma, even when Rosalina is shielding or dodging. And if we get within punching distance of it, a double Dtilt clocks ~40% damage from Luma's 50% health. I don't know why, but the first Dtilt fails to launch luma and keeps him within range of the first swipe of a second use. And our limbs are intangible during active hit frames, so trades aren't as common as with other heavies trying to do the same thing.
It's important to discuss how your character kills luma, because Rosalina without it has no chance against Bowser. And a heavyweight's high damage output puts us miles above other, sheik-er characters who deal damage in increments of 5%. We deal 10-24% per hit, with most moves separating the two characters on hit or block. Our improved offstage edgeguarding is also a big deal. But the new Uthrow combos aren't that important. Grabbing Rosalina when Luma is alive is just about one of the hardest things you could ever do, and her falling stats are exceptionally good for avoiding followups at higher damage. Thankfully most of our other kill moves are also vertical, so Flying Slam and Bowser Bomb are just as likely to secure the stock at 60-70%.
Luma being around severely hinders our jab followups. And her throws aren't weight based, so Bowser will receive maximum punishment for being grabbed. There's still a lot I'd like to lab here, but among top tiers, I feel Rosalina is the most reasonable matchup for Bowser. 55:45 for her.