Rebecca,
The first thing I'd suggest is to skip Las Vegas all together. Since between the UFOs, radioactivity, and dirt roads you don't have the most direct route available from south east Nevada to north west Nevada. The rural west isn't like what we're used to here out east with twenty different ways to go to any location from any location. So you're pretty much stuck with US-95 to go from Las Vegas to Reno. Granted it's almost a straight line but, the time it would take to drive though it, and all the little towns just isn't worth it. No matter how cool Rhyolite, NV is. Plus if you were flying into Las Vegas to gamble before hand, you can do that practically anywhere in Nevada. In fact you'll be hard pressed to find a gas station you can't play slots in.
Like others have said you don't need an RV, and it looks like you've settled on using a tent. So to the question of renting a car...
One of my close friends rented a car seven or so years ago for the burn under the age of twenty-five and is still somewhat upset about how much she was nickel and dimed. It was bad then, and can't be much better now. So why deal with the headache if it can be avoided? If all else fails, renting a car yourself could be a last resort. Just remember they will charge you for everything they can, and might even try to sneak in a cleaning fee a month later.
All hope is not lost, however. As fishy pointed out the rideshare board will be up later in the year, and even some of the info strech pointed out has some tips on the matter. I, however will point you to the
regionals page, since it will have contact info for someone in your area that can lead you to others in your area heading out to the burn as well. Some of these people might be able to offer you a ride from Reno to the playa, and back. It's also not unheard of for groups to pitch-in to rent a box truck that a couple of people drive out from your local area, that can haul larger gear (like shade that might not be able to go onto a airplane), or bicycles.
Even if no one in your area is driving out, you could always hook up with someone else that's flying in whom is over 25, and would be willing to share rental cost with. Just have that person rent the car, and avoid silly charges. Plus since they are from your area, you can meet them long before hitting Reno, unlike a stranger from some web-forum.
Like with all things, some basic logic, and common sense goes a long way when planing.
-----
edit: I knew I shouldn't of walked away from writing for so long... fishy's second post was were this topic ended when I started. *shigh*
For the bikes question, some shops in Reno rent out bikes, but that might be hard to come by.
Most people bring their own...
I'm not sure how available bikes are for buying in Reno at box-stores. I know the Fernley Wal-Mart is mostly picked clean, so I'd assume it's almost the same in Reno. One thing to keep in mind about buying a bike, or a lot of other stuff for that matter. Is almost all stores in the area have a
ZERO RETURN policy for stuff bought before, during, and after Burning Man. So you can't just buy a bike, and return it in ten days.
Is that one family still "renting" bikes in Gerlach? I can't remember if they are or not... but if they are, you could pick up on with them.
Public bikes are available on the playa. They are called Yellow Bikes, you can't miss them because they are green, and have the words "yellow bike" on them. To use a yellow bike you simple pick up one that someone isn't on, and ride it to your destination. Then dismount it, and leave it by the road in plain sight for someone else to use. You can not bring yellow bikes into a camping area.