Maybe you have really low Initiative?
Actually, it's exactly the opposite.
Units that enter combat are added at the end of initiative queue.
If players rolls higer ini than enemy and casts bilocation on him, enemy will be next one to move and doppel will move last.
Another scenario:
Players rolls higher ini and makes his move. Enemy moves and casts bilocation on player. Dopple gets added at the end of ini queue. Now it's doppel's turn, he does his kung-fu and turn ends. New turn starts and player moves again.
If player rolls lower ini than enemy bilocator, (s)he will be able to move before doppelganger.