At the moment I don't have insurance, how much would a doctor charge me for a visit to write a prescription for birth control pills

Try a Planned Parenthood clinic

There are women clincs that don't charge anything.

My doctor in Georgia (USA) charges 55 dollars for a normal office visit, and 85 for the first visit if not already a patient.

Here in China, you just go to the birth control office and they provide them free.