Hello, and congratulations on getting ready to starting your own business! Now for the hard part:
While I don't own a billing company, I know several people who do or have had billing companies, and here are how a few of them got their start:
Two got their first client right away, because they knew a doctor who needed a billing company. The other one took months to get a client. The ones that a client right away are still in business, because they then got referrals from their first client, and took on more clients. The one that took months to get a client is no longer in business, because their first client needed to be terminated due to non-compliance, and although they had referred someone else, that new client was also terminated, because they didn't do "enough business" for the billing company to keep them on.
What is important here is how these companies got their clients in the first place. Two got them through networking/referrals, and had to do no cold calling, mailing lists, etc., and they are still in business. The third ONLY did cold calling, mailing lists, website, physician office drop-ins, etc....and they are out of business. Because they didn't have an "in" with any doctor to start with.
You say that from what you have read the best tactics are mailing lists, cold calling, and simply dropping by the physician's offices. From MY experience, those don't work very well, usually. I say this not only as someone who works for several billing companies, but also as someone who manages a doctor's office every day, and deals with cold calls, mailings, and drop-in visits from billing companies(All of them are just intrusions on my day, to be honest). Others here may have had different experiences, and hopefully will chime in.
Starting a billing company and getting that first client is a very hard thing to do, because the field is inundated with others trying to do that exact same thing. I wish you the best of luck, and if you want any help down the road with landing that first client by figuring out what a potential client is looking for in a billing company, I would be more than happy to help you with that. I can "mock" interview you, as though I were a potential client, so you can see what is expected when you actually do it with a real client.