When I've done the trail, I've started at Plummer. The only potential downside is that the last 5 miles going back into Plummer the steepest, but it is a rail grade, so nothing is that steep.

Plummer is a pretty small town and I don't know of any bike place there (that does not mean there is not one, I just don't know of one). You may have to rent something in Cour d'Alene or Spokane. Since Plummer is small, I don't think I would worry about leaving a car overnight.

Sounds like your plan is to Ride to Mullan and spend the night, then ride back. If that's the case, what are you planning to do for the night?