The 2009 National Geographic Geography Bee state qualifiers were composed of 41 students (out of roughly 5800) who are listed as sponsored by a homeschooling organization. The true number of homeschoolers participating at the state level might be higher, since some of them qualify through competitions held by regular schools, but disaggregating that from this level of the data would be impossible. In any case I find it somewhat implausible that the number is much higher (over 100).
In any case, less than 1% of state level qualifiers are nominally from homeschool organizations. By contrast, 6 national qualifiers (out of 58) are nominally homeschoolers, about 10.4% (I’m including the Alaskan state champion, who qualified through a distance learning school).