I bought this plant and the lady at the nursery called it a Bat Plant. I have not been able to find any info on it. The flower looks like a bat's face. If I bring it inside for the winter, should I cut it back?

I beleve what you are describing is a , "bat faced cuphea". It is not a native but does well here. I have had it for two years and they did not survive over wintering. I would not cut it back, I think that could be done later if necessary.
Tony M