Are the terms "Rottie", "Dobie", and "Weiner-Dog" offensive too? You think "Bully" is an offensive way to refer to a Pit Bull, you'd crap yourself if you heard some of the things I call my cat.
It's just a nickname, I think you know that.
On topic - I don't really like for my pets to intermingle but if you've got it under control, do what you want. Cute pictures!