Also, BB only needs about five seconds to work out their twists, six hours to set up the isolation booths, and no time whatsoever is used for briefing the host. 
I think TAR might collect fresh applications if it had been renewed or not on a 'just in case' basis, but given the high ratings for the premiere and the sudden potential need for programming, it wouldn't surprise me if the next season's been thrown onto the fasttrack. Casting might actually be fairly quick: the killer for TAR in prep time is the planning, scouting, and verification of the course. If that's ready, they could be shooting in under two months. But if they're still figuring out the legs...