The only true combo you can do on any character is jab uptilt. Other than that, you can get a free uair on fast fallers after a koopa klaw forward throw if they DI like shiet. The rest is all reads. Of course you can combo but it's much more work.
You'll end up hitting and coming back to your neutral position most of the time.
Edit: If you release a grab, you have a 10 frame where your opponent cannot move, just enough to regrab. While they can just DI up to release mid air, if you koopa klaw release they can only release on the floor.
So yep, Bowser is a different type of character. Glad you picked him up. o/
Go watch a few videos of DJNintendo, so you'll see what you can do. And learn how to fortresshog and wavedash/land!