Following my motto of "because nobody else will", I took an indepth look at the bowser v Olimar matchup:
Facts
He can shieldgrab FTilt unless it's perfectly spaced
He's actually better off just spacing the grab, it outranges FTilt
Gimpy combo doesn't even work because he can shield immediately when the grab hitbox disappears
Just in case you didn't know you can't hit pikmin that are commanded to grab, you can however interrupt the grab by hitting Olimar
UAir, FAir UTilt and USmash cannot hit you if you space klaw correctly against a grounded Olimar
However if Olimar is at the same-ish altitude as you he can beat Klaw with a Yellow FAir and if your spacing isn't perfect a blue FAir will do the job
If you're spacing the klaw properly a grounded UpB will hit you frame 17
Olimar's movement during the initial frames of UpB is too subtle
Only reliable way to see it coming is to watch out for the pikmin converging on Olimar
Olimar's UpB sound comes out frame 7
Bowser's airdodge is only invincible frame 4, that means you would need a reaction time of 6 frames to sound or 12 frames to the pikmin grouping
The conclusion is that unless you have really good visual reflexes you have to read the olimar player's habits or mix up randomly in order to succesfully airdodge the UpB
Getting Pikmin off of Bowser's face is a nightmare: AA, Up-angled FTilt, FAir, BAir, NAir, ledge attack and fortress don't work, UTilt most of the time just scrapes them. DTilt, Dash Attack and UAir work.
Red pikmin can go through Bowser's firebreath, purple pikmin get stuck for a while then die, every other pikmin just "bounces" off and doesn't die...
If you're breathing fire horizontally (best option at close range) Olimar can SDI towards you and hit you with an UAir. I didn't manage to get FAir to work but it should, wrong positioning I guess.
Theory
If you manage to knock Olimar offstage you actually have a pretty good edgeguard game against him compared to most of the cast. If he's recovering from above: Klaw beats whistle armor, so you can jump and try to go for that and have an optioned prepared for his airdodges. If he recovers from far away/below ledge drop fortress beats purple pikmin toss, then it's just a matter of hanging onto the ledge. You don't even need to time invincibility frames if you're not at a high %.
Air-release Klaw isn't guaranteed, but he can't punish you for trying.
So the best approach to the matchup seems klaw hopping mixed with crossup fortresses/grounded klaw. Bursts of firebreath can maybe be used as a spacing tool if it doesn't make Bowser a target for pikmin toss. if pikmin get stuck to your face UAir it off, otherwise use NAir/Fortress.
Either way it looks pretty bad, I'd call it 30:70
