While I second the "leave earlier" advice above, sometimes it's not always possible. This year is one of those years for me, so we are planning on leaving Denver around 2am Wednesday morning. This should allow enough time for a fast pit stop at the Walmart in Montrose, before rolling in to claim a spot on Warner Field (just my GF and I, so not too worried about getting there right at land-grab time). You have two main options that both take basically the same amount of time (about 6 hours), and each passes though Montrose.
1. Take I70 over to Grand Junction and then south to Telluride using US-50 and US-550. (more major highways, less scenic)
2. Take the southern route using US-285 and catching US-50 out of Salida. This eventually leads you "the back-way" into Montrose. Personally I think this route is more scenic, but it is windier. Technically this way is less mileage than option 1, but still takes the same amount of time.
Of course, the times I have quoted do not factor in stops or construction delays (which are common in the High Country in June). If anyone has any inside info on possible construction delays along these routes, please share!
PS for those NOT in a hurry to get to the greatest place on earth via Denver. Experience has shown the best Bluegrass pregame is to take several days and meander up 285 before continuing south through Pagosa Springs and Durango, camping along the way. Take one of the most beautiful drives in Colorado (Durango to T-ride), and roll in to the Box Canyon the Saturday before the festival.
Listening to:
Billy Strings