One way rentals can be expensive. National Rental Cars is probably your best bet but expect to pay around $150/day (24 hr period) for a small SUV that would have enough room to carry two bikes inside. I've used National before and they are a good resource for one-way rentals, just make sure you book both legs in advance to ensure that you have a way back to Las Vegas.

For a route I suggest this one. It keeps you high enough to be comfortable but you will have to endure some hot places. Cortez tends to be hot in July as does Delta and Montrose. The route does go past Mesa Verde and the Black Canyon of the Gunnison. I would suggest that you not ride into Mesa Verde because it's a 30 mile (one-way) trip to the ruins and camping is available at about the half way point. There is a lodge about 10 to 15 miles from the ruins but, either way, it's a couple of bicycle days of riding to get to see anything.

You could rent a car in Cortez from Enterprise, do the trip in one day and then be on your way the next day. Enterprise will pick you up from a hotel or even a campground within 20 miles of their offices and their rates are very good. I'd almost suggest the same for the Black Canyon. The rim of the Black Canyon is more bicycle accessible, however, and wouldn't be a bad ride. You might not want to East Portal Road, however. It drops down to the river but you have to climb back out and it has some very steep sections.