I recommend getting an older dog. If the rescue groups don't have a lot of bull mastiffs, take your time and look other places (shelters, online, etc) until you find one.

I have a boxer that I got off craigslist for $50 when he was 14 months old, from someone who was moving and couldn't take him. He was completely housebroken, good with cats, didn't chew, knew basic commands, and slept all night. I've had him for a year now and he's been a great dog. I am SO glad I didn't get a puppy - my husband and I both work all day and wouldn't have had the time or willingness to properly train and socialize one. An adult dog, we can handle.