I suggest contacting the school district to learn more about its transfer policies. You might also contact the charter schools to learn more about their enrollment policies (and deadlines). You may use SchoolFinder to locate the contact information for U.S. school districts and schools. http://www.education.com/schoolfinder
I also suggest asking about kindergarten orientations for the schools you're considering to learn more about them, meet other parents and families entering kindergarten at the school (as well as parents of children already attending the school), and get familiar with the campus, principal and some teachers. Below are some additional informational resources you may find helpful for this stage of your child's education (and to help address your concerns about bullying at school).
Thank you for asking, and congrats on this special milestone for your family!