There is no public transit from Nederland to the Hessie TH during the week unfortunately. (Weekends is another story http://www.bouldercounty.org/os/parks/pages/hessie.aspx)
However, the RTD system does go into Nederland. From there, it is a fairly easy hitch out of town to Hessie. You won't be the only one to his this TH, even during the week.
As for the mileage schedule, 10-15 MPD is doable for most people. However, do you plan on acclimating a bit before going to 11k+ ft? The elevation could have an impact on your schedule.
You will be above treeline for most of the trip, buy a good map does show the side trails to bail into the trees / lower if need be.