Access to Birth Control Act This bill requires pharmacies to comply with certain rules related to ensuring access to contraceptives. Specifically, pharmacies must provide without delay a customer with any contraceptive or related medication that is in stock. If the contraceptive is not in stock, the pharmacy must immediately inform the customer and either order the contraceptive or refer the customer to a pharmacy that has it in stock. Laws in some states provide pharmacists with the right to refuse to dispense contraceptive-related drugs on religious or conscience grounds. Pharmacies may refuse to provide a contraceptive to a customer (1) if the customer lacks a valid prescription for a prescription contraceptive or is unable to pay for the contraceptive, or (2) based on a pharmacy employee's professional clinical judgment. The bill also establishes a private cause of action and civil monetary penalties for violations of the bill.