Cool! BM is not like other festivals you might be familiar with. There are no official stages, and you do not need permission to play. Really, the only restrictions are on sound levels depending on where you are, and even those are pretty vague.
Basically, you just need to find a place to play. If you hunt around you should be able to find a map of the city - it's a semicircle. The first couple of streets in from the center are where most of the interactive stuff is happening. In order to camp on one of those streets you need to go through the theme camp process which might be a bit much for your first time. If you arrive along with most of the rest of us after the gates open Sunday night, you'll likely have to find a spot on one of the outer streets. There's nothing wrong with those streets, but people may be less likely to find you and your neighbors may be more sensitive to you playing really loud at 3am, if you're into that sort of thing.
One option is to haul your gear out onto the open playa (part of the big circle that isn't filled with camps) and just start playing. You can't drive your regular car, so you'll need to bring some other means for getting it out there or recruit an art car driver to help you out.
Another option would be to hook up with a camp that is already setting up a stage and get them to let you use it or become a part of their camp. Hair of the Dog is one camp that sets up a stage for anyone to use, there are likely others who would love a band. I'd say start posting here and on tribe next Spring that you are looking for a place to play. Once you have a time and place arranged you can get it put on the official list of events. Even if you aren't able to work something out ahead of time you can likely arrange something on-playa and gather a big enough crowd. There's plenty of people who just start playing for the fun of it.
Do you have your own equipment (including a generator!) or were you hoping to use a house system?