Doing Interstates gives you the option to ride some really nice roads once you get there, South Dakota and Colorado are awesome. When I went in that direction, I bombed down the I90 and was in Rapid City, SD in two days. Went south from there. If you want to stretch it out, you can ride the north shore of Lake Superior, maybe hit some roads in northern Wisconsin, then boot across the I90 to Sturgis. I'd probably spend as little time in the midwest as possible.

Problem with doing side roads is that your progress is cut down by about half, no way you'll hit Sturgis in three days without riding like a bat out of hell. Google maps shows 2350km being the shortest route. Assuming that route, it's still almost 800km per day. 800km with food and gas breaks comes out to about 10 hours of riding for me.