I have my B.A. in Spanish and hope to gain experience and a good resume while teaching English in Spain. I also have a CELTA certificate from International House. I'd love to teach in a private school in the U.S. if it means I won't have to go back for a 2nd degree right away.

Each state has their own requirement for certification. Private schools often have their separate requirements, so you would need to check with the school and/or state you wanted to teach for. The real need in public education for someone with your skills is not in teaching Spanish but in teaching English to Spanish speakers.

¿De verdad quieres volverte a USA?
¿Tienes nostalgia o es que te tratan muy mal en España?

Ser profesor de español.... ¿ya lo dominas? ¿O sigues teniendo ese acento tan típico de los states?

Buena suerte

You will need to check with the specific state's Department of Education for their requirements. Most states will require your B.A., some teaching experience, a fingerprint check, and a passing score on an examination (National Teacher's Exam/PRAXIS or a state-specific teacher's test). Google a state's name and "department of education" for more information.