The earliest you'll detach for BRES is the end of February, so that equates to about 7 months. You won't find out until the fall when you'll be sent to BRES (either the class that starts in March or the class that starts in September), so there is a chance you'll be at NRHQ for over a year before detaching to Pittsburgh.
Most engineers sign a year-long lease, and break the lease when they get orders to BRES. Make sure whatever lease you sign has a military clause, which will protect you from paying absurd fees for breaking your lease. If you have more questions, send me a PM.