Actually the best way to get to Musselburgh from Edinburgh is by bus. The 26, X26, 44, 113, 124, X24 but not the 30 all take you along the coast road from Eastfield to Levenhall. The 26 and 44 leave from South St David Street, the others from outside the Apple Store across the road from Waverley Steps. Musselburgh Railway Station is quite far from the coast. The White-winged Scoter has been mainly off Fisherrow, on the west side the river, there have been 2 or 3 Surf Scoters too but they have been seen at both sides of the river.
David