There are some (few and far between) apartments and condos that rent to adults, but there are always some students mixed in with them. Colleague of mine lives in some pretty nice ones out near the airport that are about $1500 to start for a one bedroom apartment. Other colleagues swore by a condo complex near or behind Johnny Carino's on Harvey Road, but that may be to buy only.
Techno is right, your best bet is to find a house to rent. I have very very rarely come across anyone around here who is happy with the apartment situation in BCS.
Which is why (not to reference another thread) the much maligned Stylecraft Homes are an attractive option, positioned as they are between the McMansions of Pebble Creek and the student or thug apartment complexes/projects.