We have discussed this topic a few times, including on our Medical Coding and Billing Blog, for most who eventually started their own medical billing business from a home office it was not something that happened overnight. They have been in the field as an employee with trusted employer relationships for years, and have made contacts with doctors and clinics who have earned their trust. This would be the point where one could say: "Doctor So-and-so, I am looking for opportunities to do this job from my home office. Would you allow me to take some of your billing home."
So, in a nutshell, your education counts, experience counts, employee relationships count, and trust and references count. Then, when you have all this under your belt make sure your resume is updated and shines, also make sure you have researched and know local and state laws as to what is required via city ordincane and zoning, and such, to run a home business. Find out how to incorporate your business. Although you could "freelance" it, an LLC provides you with a certain amount of protection.