Yes, you should bathe a cat. How often depends on the health, age, and habits of your cat. People with animal allergies react to the proteins in the skin dander. However, more people are allergic to cats because they also cover themselves with saliva which also has proteins.
Just for fun I put together a little infographic comparing professional cat grooming with old fashion spit and tongue.
If I licked myself all over would you hug me?