If I award a bounty, and my rep therefore goes lower, do I lose the privileges I've earned? For example, if I was just at 1001 Rep, and put up a bounty for 50 Rep and awarded it, do I lose my privileges for having 1000 rep? Or does it stay there since I did eventually earn it?
Privileges are not permanent.
If your rep falls below the required threshold of a privilege for any reason (you place a bounty, downvotes, rep recalc, beta→gold site transition, etc) you do lose the privilege, but only until your rep increases above the required threshold again.