Kiwanis program reported sold out, but just checked and see that now (Aug 19th, 2011) their site says "We also have a limited number of bikes for sale on-site for anyone who didn't make a reservation."
.http://www.kiwanisbikes.org/burningman.htm"Bikes available are ready to ride and are sturdy enough to survive the playa. ... All Burning Man bikes are $30-$50.... Hours will be 9:00am - 9:00pm During this Period"
The bikes are good enough (you pick through them to find one you like, then they check it out mechanically before you leave), and you don't have to feel bad about them getting trashed by playa dust. Personally, I recommend getting one with BOTH brakes working, even though you won't be exceeding the BRC 5 mph speed limit.
Additionally, they usually have a few bikes for sale at the Save Mart on Keystone.
If you're really stuck and end up without one in Reno, watch the route along the way to the playa for individuals selling bikes at the side of the road and in Gerlach.
And if worst comes to worst, there's the BRC Yellow Bike program.
(starting to see more and more warnings about traffic on the I-80 in Reno while it's under construction)