Can you stay in the bus when it’s on the ferry?

For crossing the Channel, definitely not. A very special exception can be made with prior arrangement for those with disabilities that made entering & leaving their vehicle too cumbersome, but they aren't going to ride this kind of bus.

No, but you can when the bus is on the train in the tunnel.

This was in the 50s; the tunnel still wasn't far off science fiction at that point.