The detour around this closure involves many miles. Check with the inciweb website (listed above) before making a decision as to what to do. MT DOT wants to get the highway open again as quickly as possible and conditions change daily. The detour starts in Missoula: follow I-90 northwest to Mullan, ID. This will include some frontage road riding and some interstate riding. In Mullan you get onto the Trail of the Couer d'Alenes, a 70+ mile paved rail trail going west to Plummer, ID. From Plummer, take US 95 south to Lewiston, where you reconnect to the Lewis & Clark Trail.
Idaho has a bicycling map. Here's a link in pdf format: http://itd.idaho.gov/bike_ped/BikeMap2010.pdf