But I've actually played this matchup. D=
Good Bowsers will generally try to keep you outside with well-timed Jabs and tilts and Klaws and Up-B out of shield. Aerials are rarely ever used except in some situations for punishing air dodges and edgeguarding. If you're forced to go on the offensive, then this matchup swings in his favor yes.
The matchup is pretty simple however since you're trying to get Bowser to approach, and his shield is not so good since it will get poked easily especially if you're fireball camping a lot.
If Bowser is coming from the air, the way he approaches happens to always be in range of your Up-B. Keep that in mind, since this is invaluable for punishing him before he liek klaws you or whatever.
Keep that F-smash ready to punish ANYTHING he whiffs. Not only does it do 18%, it will get him offstage 95% of the time if he already has some damage on him. And Bowser going offstage is of course an opportunity to cape him. If you Cape him, even if he has his midair jump and his Up-B after that, it's very difficult for him to get back. Having a fully charged FLUDD makes this already fairly easy task even easier, not to mention Fireball spamming.
Don't get surprised by his Down-B. Just keep in mind you can always air dodge the ground version.
The main headache in this matchup is in close range where you're trying to bait him out of his shield or poke him once it is worn down, but when it comes to maintaining momentum, Mario more advantaged here as far as I'm concerned.
The rest of this matchup is pretty obvious, when it comes to maintaining momentum, comboing, and stuff, and is something that should come naturally to most Mario mains.