I don't know Hendersonville well, but I know that you'll have trouble trying to get into Asheville charter schools at this point. They are very popular, and tend to have long waiting lists. As for private schools in the area, you should look into:
Carolina Day School
Carolina Day School
The Learning Community
The Learning Community School - Asheville's innovative, private school for grades K-8
Rainbow Mountain Children's School
Asheville Private School - Preschool Through Middle - Rainbow Mountain
The Odyssey
Odyssey Community - Asheville's Private Integral School
Asheville Christian Academy
Asheville Christian Academy » Home
I don't have personal experience with any of them, but have had all of them recommended to me by at least one person. They are very different in terms of philosophy, curriculum, and price, so you'll need to figure out what best meets your needs.
I hope that's helpful. Good luck!