The Idaho Bicycle/Pedestrian Coordinator offered a couple of alternative routes to avoid the shuttle and the construction on I-90:
Northern Route (going westbound)
Exit I-90 at Regis, MT. Go east on Hwy. 135 to Hwy. 200. Go north to Thompson Falls. Turn west onto MT Secondary Hwy. 471 to Thompson Pass. Continue over the pass into Idaho passing through Murray, Prichard, Enaville and Kingston. Rejoin I-90 at Exit 43. The road is paved all the way, very scenic and frequently used by cyclists.
Southern Route (going westbound)
Note: There is no viable southern option for road cyclists.
However, if bicycles are set up for gravel, i.e., a mountain bike or a bike with at least 700x32c tires; there is a much shorter detour—only 11.5 miles. It is the NorPac Trail. Details can be found at http://friendsofcdatrails.org/maps/for_all/09_NorPac_Trail.pdf
Going westbound the trail starts at the Lookout Pass Ski Area on I-90.
For more information see this blog post from June 2015 on the first half of the project: