Remoter regions of old city swinging both ways in middle of Texas (7)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

UR (city in ancient Mesopotamia, now southern Iraq) + BI (short for bisexual = swinging both ways), inserted into the middle letters of [t] EXA [s]. Further out than suburbia: commuter areas around a large city.