What do you think of my chances of transferring to a private university?

private universities really want your money right now so I would say your changes are very good if you can afford the prices make sure you fill out you FAFSA early and check with the school for early enrollment discounts and school offered scholarships. the earlier you apply the more likely you are to get the extra funds. your grades sound good and with your volunteer work you should be fine. If it is a religious school you may need a recommendation form a priest or church.