I don't know much about Sonic, but I'll throw Bowser's options in here, anyway.
Bowser has his incredibly fast Jab. Unfortunately, many Bowsers underestimate the awesomeness of our Jab. But it's really good, incredibly fast and has good range - for a Jab at least. His FTilt is pretty quick with good range, priority and knockback, so don't underestimate that, too.
Basically, you don't want Bowser on the ground. You also don't want to be in front or above him. This is where he excels. UTilt, USmash and UAir are some of his most reliable killing options and deal a huge amount of damage.
Klaw Hopping and Klaw Dropping can be issues for Sonic - if you get SideB'd, you'll be Bowsercided or get ~20% damage, so be aware of this. It's inescapable.
His shield is godlike, and he has one of the best OoS options - UpB, which has invincibility frames. It most likely will be used retreating to the ledge, so the cooldown is cut off.
Fire probably won't be used much against Sonic due to the fact it's rather laggy and can be punished, so don't really mention it. It, though, probably could be used as an edgeguarding option to throw in a few %s of damage, or for forcing an approach.
Sonic probably won't see many FSmashes. They're only used if Bowser is definitely secure on hitting with it.
I won't even start on the Grab Release shenanigans, lol.
Basically, Sonic has to avoid and run away from Bowser and punish him quickly for wiffed slower attacks. Bowser's quicker than he seems, so don't think you can run in, hit and run away again. He'll get you.
Additionally to this hit and run tactic, Sonic has an extremely hard time killing off Bowser - Sonic's reliable killing options all are rather laggy, and Bowser usually is a master in shielding and powershielding. Sonic also has trouble pressuring Bowser, as the turtle can literally stay in his shield all day long.
Keep in mind that almost all of Bowser's moves are capable of KOing.
If you have any questions, I'm willing to answer.