You have got to get a skip the counter option. Book Enterprise or Alamo more than 24 hours in advance to get a skip the counter message/e-mail (you have to do online check in first, then next they should send you some skip the counter link to use to actually activate skip the counter), use National (Emerald Club), use Avis Preferred or Budget Fast Break...
Using one of the low cost rental car companies at DEN- good luck. If you are arriving at an "off" time that isn't busy it may be okay but if you are arriving at a busy time forget it. Or prepare to wait two hours. I have done this a couple times at DEN. I won't do it again. Their busses also are very slow and seem to run with a lot less frequency. Unless something changed this year, at DEN, the bus is run by the rental car company individually (not a consolidated bus). Stick with the major companies...