What is wrong with "Bu bavulum değil"?
I just kind of sounds wrong :D The issue in question here is that you are stressing that it isn't MY suitcase. In this case, since you are stress the ownership of the suitcase (or lack thereof), it can't really be dropped.
Adding to this;
Benim can only be omitted in a context like:
"Bu, bavulum değil; çantam." (This is not my luggage, it's my bag.)
Can we say "Bu benim bavul değilim" ?
Can we say Bu bavul değilim?
:D yes. And that would mean: I'm not this suitcase! I'm actually that luggage over there.
" bu bavulum yok " ?
it is like "My this suitcase does not exist" - so it does not have a meaning
That's kind of like "this ... I don't have a suitcase"