How long is your BOLC? If it's one of the longer ones like Military Police, I'd guess you have plenty of time. Either way, if you have BOLC dates, I can't see why you would be coming back to where you currently live.
My daughter had BOLC at the same base as her 1st Duty Station so once she finished BOLC, she had to report to "work" a week later. That made things easier because we just went out a week before BOLC started and found her a permanent off-base place to live. My son has BOLC that starts this September in Virginia and ends in early February. His orders are to report to Fort Hood exactly one month later so that should be plenty of time to get down there and find a place to live.