Hi and welcome, I am not really sure what to suggest, maybe you shouldn't have got a cat if your parents didn't approve ad with the hamsters I don't find it fair that you just want to get rid of them now that you have a cat,I don't mean to sound harsh but if you have any pets you should want them for the whole of their life.x
I am guessing that Bowie doesn't like to be confined. Anywhere a cat is not supposed to go to, that is where they focus on.
I live in an older home with a sump pump and we have a concrete hole where water from our washer drains into. I am petrified that one of my kittens will be enticed by the shiny water and fall in so I keep the door shut. Every chance they get, they try to sneak down there.