Green’s Dictionary of Slang

1. one who moves from place to place [mush v.¹ (1)].

1902		J. London ‘Rods and Gunnels’ in Bookman XV (Aug.) 541–44: These are the canaille and bourgeoisie, these ‘gay cats,’ ‘bindle stiffs,’ ‘stake men,’ ‘shovel bums,’ ‘mushers,’ ‘fakirs’ and ‘stew bums.’.
1905		R. Beach Pardners (1912) 27: I heard voices in the cabin. ‘Some musher out from town,’ thinks I.
1907		J. London Road 60: There were two more in their gang, who were across the river ‘mushing’ in Harrisburg. A ‘musher’ is an itinerant fakir. This word is not to be confounded with the Klondike ‘musher,’ though the origin of both terms may be the same; namely, the corruption of the French marche ons, to march, to walk, to ‘mush.’.

2. an itinerant fakir [abbr. mush-faker under mush n.³ ].

1907

see sense 1.