I posted before on why Peach is the worst matchup for Bowser so I'll post it again and also add some things about Sheik.
Peach is Bowser's worst matchup. Yes, its worse than Sheik. Bowser can't combo Peach for ****. If Peach turnip camps him, especially if she's using a platform right above her for extra protection, its mad hard for Bowser to reach her. If the Bowser tries to use the strategy of grabbing the turnips and throwing them back to her to help approach, it will barely help or no help at all. Bowser throws mad slow. Her down smash destroys him and if she hits Bowser with a down smash at 0% or very low percent, he can get grabbed to continue getting combo'ed. Bowser can't tech chase her since she's a super floaty. He also can't do anything out of forward throw claw because it pops her up too high. Bowser regular shield sucks and Peach's down smash can suck you in, so he ends up getting clipped alot. She can float cancel combo him hard since he's such a fat ***. Its tough sometimes to even land an up-B outta shield since she's can be mad homo approaching from the air all the time. I know this happens with other characters but it happens alot with Peach. When you manage to get an up-B outta shield on her, it'll do the initial hit but then clip her with another part of his up-B. Since Bowser's recovery sucks, she can easily edgeguard him with either turnips, float cancel nairs or pretty much whatever. Bowser has mad trouble edgeguarding her and thats one of Bowser's main strengths. Bowser's main kill moves on her are his up-tilt, down smash, and forward smash. Peach is the #1 character in the game that gets caught by Bowser's forward smash. One example is Peach approaching with a float to fair. Bowser backs up, with good spacing and timing avoids the fair and hits Peach.
As for Sheik, we all know how you can get chain grabbed like crazy. Although if the Sheik messes up the next down throw chain grab by even the slightest frame, the Bowser can jump out. I've played plenty of Sheiks, including M2K's to verify this. The best way of getting out is of course DI'ing directly above Sheik and trying to time your jump perfectly. I know its hard to approach Sheik since Sheik can just f-tilt and fair all day. Although its not as bad as Peach. Bowser getting edgeguarded by Sheik is pretty gay too because of needles and such. Now Bowser at least has some good combos and setups against Sheik. Bowser can tech chase Sheik, which is pretty convenient. If Bowser gets Sheik with a claw, does the forward throw and the Sheik has a good amount of percent (lets say about 60% on Yoshi's Story before the claw grab), Bowser can get an up-air kill after the forward throw claw pops Sheik up if double jumped after the forward throw claw at perfect frames. Sheik cannot get out in time if done correctly. This combo setup also works on Marth. Bowser can also gimp Sheik in even two moves if done correctly and it also depends on Sheiks recovery. If Bowser claw grabs Sheik from the ledge at 0% to very low percent, the Bowser does the back throw then proceeds to take Sheiks second jump (one way is jumping off stage and fairing Sheik's second jump), then grab ledge again and Sheik won't make it. We all know Sheik's recovery isn't that good when you force her to up-B back into the stage while you're grabbing ledge. Since Bowser's main strength is edgeguarding and he hits mad hard, edgeguarding Sheik is definitely helpful for him. A couple options is just grabbing ledge and either bairing or claw grabbing Sheik and doing the back throw immediately so they probably won't DI. Back throwing immediately after getting a claw grab and they don't DI because its so fast is the main reason WarriorKnight and I don't bite most of the time when getting the claw grab.
Sorry I don't have videos of me playing Sheiks or Peachs in singles. I rarely ever end up getting recorded. Although this is my feedback on why Peach is Bowser's worst matchup and not Sheik. Sheik is still and will always be an extremely horrible matchup though. As a quick thing for the Young Link matchup, its possible to maneuver around the million projectiles and end up getting through to Young Link. I've played many Young Link players over the years that range from really aggressive to extremely patient and campy to just plain "I'm never going to approach you and just throw projectiles this whole match". Trust me, its possible and its not as bad as you think. You just have to know the matchup and have good maneuvering capabilities with Bowser.
So thats my input. WarriorKnight and I talk all the time and play once in a while and we agree on everything since we've been playing the highest level of Bowser for years and have vast knowledge with the game and matchups, especially me since I know more than he does. I was even thinking about bringing back Bowser when I return to playing in tournament again. Who knows? I hope this helps.