The doctors are witholding a prescription that most women are not willing to give up in order to have an unrelated test done that the doctors know most women would refuse otherwise. It is a bribe.
It certainly is not a "bribe" as that term is meant in the law. Clearly you don't like the doctor's position, but it won't help to distort what's really going on here.
It's no different than any other business situation. You go into a store and want to buy just one product, let's say a shampoo, but the store insists on selling the shampooh as a package with a conditioner. You don't want the conditioner, you think it's worthless. You don't have to buy the package deal, of course. You can go to another store that sells just the shampooh you want. What you can't do is FORCE the store to break the combination deal and sell you just the shampooh because no law requires that.
Your situation is exactly the same, only in this case the "products" are the birth control pills and the pap smear test. You want to buy just the pills; the doctor wants to sell you the package product. Just as with the shampooh, you are free to go to another doctor who will give you the birth control prescription w/o the pap smear, if you can find one to do so. But like the circumstance of the store selling shampooh, you cannot FORCE the doctor to do what he doesn't want to do and give you just the birth control pill prescription without the pap smear test. The principle in the both cases is the same. The fact that this is a doctor's office and not a retail store doesn't radically change the law here and give you the power to dictate to the doctor how he provides his services. Bottom line, if you don't like the doctor's position, walk out and go to a different doctor.
Lastly, why is that women are allowed to KILL their unborn children and they supposedly have the right to choose this, but I don't have the right to refuse a test that I am well informed about?
You are comparing tomatoes to moon rocks here. A woman's right to an abortion as decided by the Supreme Court in Roe v. Wade, 410 U.S. 113 (1973) was a decision that held the GOVERNMENT could not prevent a woman from getting an abortion. Prior to Roe, many states had criminal laws against abortion—after Roe, those laws could not be enforced. But the Roe decision does not compel doctors to provide abortions if they choose not to engage in that practice. A woman cannot FORCE any doctor to give her an abortion against the doctor's wishes. What the Roe decision simply says is that once she finds a doctor willing to do it, the government cannot lock her or the doctor up in prison for doing the abortion procedure. Similarly, you cannot FORCE a doctor to give you a birth control pill prescription against his wishes. What you can do is look for another doctor willing to do it, just like the woman seeking an abortion can go to another doctor if her present doctor will not do the abortion procedure. Yours is not a case of the government criminalizing birth control pills. If it was, then Roe and the abortion issue might be an apt analogy. As it is, Roe and the right to an abortion simply have nothing at all to do with the issue you are presenting here.
I understand you feel strongly that your doctor is wrong. But both you and your doctor have the freedom to decide with whom you will deal in your business relationships, and that is what this is, a form of business relationship. Just like the shampooh example, you both have the right to walk away from the deal—no law forces either one of you to deal with the other. That's about as fair as I think it can get.