No, you don't need to bring a partner. In group classes most studios rotate partners, and in private lessons you'll dance with an instructor.
In my area, group classes are US$10 and private lessons between $50 and $65 per hour at the independent studios, with group packages a bit more at franchise studios. I've paid quite a bit more for a special coaching, but that isn't something that's needed, or even to be thought of, at the beginner level.