As the owner of two pittie mixes, I feel your pain. Finding a place to rent that would allow bully breeds was a pain in the rear and our older dog looks like a Bull Terrier without the egg-shaped head. Other than that, she's the spitting image of a Bull Terrier.
My best suggestion is to start looking now, call the rental agencies and ask if they have size/breed restrictions. Be prepared to bring along 'references' for your pets from previous landlords if at all possible. Check your local craigslist for pet friendly rentals, post in the wanted or pet section to see if the community can help, they can be amazingly helpful.
As a mixed breed it's easier, but be prepared to always be asked that question and even get told you are lying if you try to explain it away. I would just be honest about her breed, if you know it, that way there would be no question about your integrity should there be a question in the future. Especially if she's as sweet as she looks, if you know she's pittie, say it loud and help end the stereotypes...that's what I'm trying to do, one person or one trip to the dog park at a time. LoL.
As a military wife, we are going to get moved a lot (we've lived on base up until now) and I fully intended with the current landlord to get a 'reference' from every single one we have from here on out. No damages, no problems, hopefully will mean no future hassle about having dogs bigger than a cat! LoL.
Good luck with everything
It is true that Pit Bulls grab and hold on. But what they most often grab and refuse to let go of is your heart, not your arm.