Black Rock City is a big place. There are three main ways to get around it:
The playa is hard on bikes. You should choose the cheapest, simplest bike that works reliably. The ideal bike is a cheap beach cruiser with fat tires that won’t sink into the sand, no gear shifters, and pedal brakes.
From a practical perspective, preparing your bike is easy: if it works at home, it’ll work just fine on the playa. If your bike doesn’t already have a kick stand, you may want to add one: it’s often hard to find an empty bike rack.
Just like at home, lights are absolutely mandatory if you’re riding at night (which you will be). You can use standard bike lights, or go for a more elaborate and artistic solution. Many people use El-wire to decorate their bikes. One handy solution is to mount a flashlight holder on your handlebars. That way, you can use a single flashlight whether you’re on foot or on your bike.
Burning Man isn’t just about practicality, however. A plain, undecorated bike is an eyesore and a civic blight. At the very least, take the time to spray paint your bike an interesting color. Even better, take the time to do something really visually interesting with it.
Bike theft is a significant issue on the playa. You should keep your bike locked at all times to avoid having it “borrowed” by a clueless person without a bike of their own. Pretty much any lock will do, but you may find it convenient to use a combination lock, so that you don’t have to carry a key with you.
You don’t really need to carry a lot of bike tools with you: if your bike dies while you’re out and about, you can just walk it back to camp to fix it. There are several excellent camps that can help you with bike repair, but Burning Man's radical self reliance principles still apply. The bike camps exist to give you a hand, not to do your work for you. Don’t take them a junk bike and expect them to magically overhaul it for you.
At a minimum, each camp should have a good set of basic bike tools and a good air pump. Make sure you have a spare inner tube that fits your bike.