Going to a Gynocologist?

I doubt your KP insurance would cover the fees. KP's operational model keeps patient care as centralized and within their walls as posible. If you want a cheap Pap, I'd recommend you look into getting one done at PP and pay out of pocket (it won't cost much for you 'cause you're a student), call Santa Clara County public health and find one of their clinics, or go to a student health services clinic on campus.