These races are still going on. They take place on the 1st Tuesday of each month. The next one is on Aug 4th. Its from Minnewaska to near the end of Clove Road, just under 8 miles. We have no rules on types of bikes, but I'd say you would be going much slower on a mountain bike.
If you want to get in more information sent about these races send me a PM with your email address. I'll add you to the mailing list.