The left-hander has to fly home at 10.30pm on the same day to join a training camp in preparation for Australia's short tour of Sri Lanka, which may not go ahead because of the political situation on the island, and Yorkshire's request for a 24-hour reprieve has been turned down.
Essex, who play Surrey at The Oval in other semi-final, are in the same position with their own prolific batsman, Stuart Law.
Yorkshire's cricket chairman Bob Platt said: "Much will depend on the weather. If it is a good day with an encouraging forecast, Bevan will play. We will, however, have two players standing by as cover."Reuse content