I'm sure not much has changed since when I played, so I'll say this:
With Bowser you need to find a balance between aggression and defense. Bowser's defensive/ground game is extremely fearful and is above average imo...lol in a perfect world at least. To be more serious, it's pretty good for all the other **** he has. He obviously has inherent flaws, but his OoS game, grab/klaw gimmicks and things like that are helpful.
To be as frank as possible, playing aggressively with Bowser is ******** (am I allowed to say that word). If you don't have the means to capitalize on some grand mistake or some other flaw that the character has, (or if you're just better, then that's an exception ololo) it's not worth going in.
Klaw is the move that can convert defense into offense. Use it. It's a great move, kids.
To add on, you shouldn't worry at all about taking a while to kill your opponent. As long as you're doing the right things, the kill will come eventually. You have 8 minutes, if you need to take a breather or switch the momentum of the match, go ahead. There's no reason in rushing the kill anyway, Bowser is a powerhouse but you have to find a specific way to get each move off to get the kill anyway.