In terms of Bates, on the page for homeschooled applicants, it doesn’t mention requiring standardized tests, although other requirements are listed - obviously, I would contact the school to be certain, but here’s the page in question http://www.bates.edu/admission/home-schooled-students/
And of course,for Bard, if you take the Bard Entrance Exam route, then no testing is required http://www.bard.edu/admission/bardexam/
Finally, I think that what some of the posters here are suggesting is that when you have interviews, be careful that you don’t come across as too inflexible or superior. Accept the possibility that your views are not necessarily correct or better and be aware of the fact that your education might not have been better than what is available in public or private schools, just different.