Just logically thinking if Bush were to stay I think Lake would have stopped speculation. At presser he didn’t even mention Bush. Said there will be several changes on staff and on offense after the bowl when he’s officially head coach.
I get you don’t discuss entire coaching staff at presser but in this situation if he was planning on keeping Bush he would find a way to mention Bush. “I’ll sit down with Bush and go over what I’d like on offense” something along those lines to basically tell everyone he’s coming back.