We are homeschooled as well. We have one particular parent that is just incredible at getting sponsorships. She got them from local government agencies like BAMA (Bay Area Manufacturers Association) and some business. Use the word STEM a lot, it's the catch phrase of the day, show your successes from last year. Try and get the local paper and/or TV station to do a story on you and your team (works well asking for sponsorship then), they are always looking for neighborhood feel-good stuff. Check with your local University, see if they will pitch in $500. For us, get rid of the "show up in a tie and ask mentality". Get a good team polo shirt with khaki's and be realistic when presenting, otherwise you look like a used car salesman. They know you don't dress that way.
Show the business your robot. Doing a flyer is fine, but have at least a minimal website you can direct them to that has your videos, awards, pics, etc.... Do that first. You only get one time to make a first-impression, and that website may be it.