No, you don't need a partner. If you have a partner, bring one. People often come by themselves and find partners here, sometimes with the assistance from the instructor.
You don't need a partner all through the class. We teach steps separate to ladies and men and we make sure one knows her/his steps well before joining in with the partner. Dancing with different partners helps you to dance better. Don't be afraid to ask more experienced students to dance. They are very willing to help and encourage beginner dancers.