Here's their document about seeking sponsorship.
.PDF warning http://www.capitol-best.org/CD/Resources/BESTsponsorship.pdf
Here's what another team has put on the sponsorship section of their website.
There are several opportunities for which you can support our team. First, our Oak Mountain High School robotics team must design and purchase tee-shirts for competition. Second, in order to practice for the competition, a mock up playing field must be constructed. Third, as we build and test the robot, the team needs additional consumable resources such as plywood, nails, screws, and other components which are purchased at local hardware stores. Fourth, the team must construct a booth to display at game day. The booth is used to market our robot. Each of these activities requires a great deal of funding. We invite you to become part of our team by assisting.http://www.omhsbestrobotics.com/sponsorships
From reading the BEST website, I gather that the teams are given no information about the rules for each year's competition until it kicks off - that's when they find out the nature of the robot they have to build, what materials are in the kit provided, etc.
Your cause would have been helped by including this kind of information in your OP.