Rather than getting dropped into the game at a stop, why not have the joining rider’s Avatar inserted into the game as an AI rider who is in draft position of the leader/rider being joined? The joining rider’s Avatar should be matching the speed of the joined rider.
Over a period of ten or twenty seconds, the joining rider can then gradually spool up their output on the trainer to match that of the AI representation in draft. As the match is achieved, there could be a cool animation effect of the AI transferring into a real rider. (e.g., Matrix like morph effect, meteor or lightning strike, etc.)