I've got the bus back from Musselburgh after the other ½ marathon (not the one on Saturday,there was another at a different time of year that also finished at Mussy) and never been a problem.
My other half normally parks the car up near the High Street, and will be doing so again this Sunday, normally some queues at the bus stops but nothing too bad. Put it this way, if it was a choice betwen booking one of the overpriced shuttle buses the organisers put on or catching a normal one I know I'd pick the normal LRT ones every time.
Local boy here. Mate, I would park in town where the race starts and then after the race, head up to Musselburgh High Street (5mins walk from the race finish) and get a local bus back - there's quite a few to choose from, you may have to wait a bit cos they'll be busy, but that's what pubs were invented for . . Oh, and they won't get disrupted by the race, the roads are open round that way.