You can walk from Euston to the museum in around 15 minutes which is often quicker than the alternatives. Turn left on to the busy main road in front of the station, past the fire station, the British Library, St. Pancras Station, and King's Cross station. Then follow directions as from King's Cross.
Bus 91 runs from the bus station to Wharfdale Road, a two minute walk from the museum. Routes 10, 30, 73, 205, 476 go from Euston to King's Cross. Routes 30, 73, 205 and others are fully accessible to wheelchair users.