It's certainly doable on a bike, but I'm not sure I would recommend bringing it if you can park it nearby (Reno?) and get a lift in.
You can carry in enough food and water, but one thing to be aware of is it will be hard to get out of the elements if you just have your bike and tent.
If you are there for any amount of time, the wind will usually whip up and there will be a mini sandstorm that can go on for minutes or hours. You can easily survive it but on occasion it is just nice to be able to get out of the wind and into a place that is somewhat sheltered.
Connecting with a theme camp that has a big shelter tent can certainly be enough for you, but I noticed a few forlorn bikes that were in the elements for a few days and since everything gets coated with a fine powdery dust the bikes didn't look too happy.
All small issues in the end though, BM is not to be missed. You can just rock up, and if you haven't found a camp prior, you will get directed to a section with a bunch of unaffiliated people like you. You'll meet a thousand of friendly folks and from there how everything ends up cannot be predicted
You'll understand better after you go...