Question: I have worked for public interest law firms for nearly 20 years. It is possible to transition to private practice, or do I have to hang up my own shingle?
Answer: I think that anyone who has worked in public interest for 20 years has the ability to do whatever they want going forward.
The key, whenever applying for a law firm job (or any job) is to show the potential employers what you can do for them. How you can be successful at the job. How you can bring in money. Why the partners should hire you.
Your next step will depend very much on what kind of experience you have and what you are hoping for. It will also depend on what kind of contacts you have developed and what kind of rainmaker you can be.
I think what you need to do is sit down and look at what is expected and needed in a private firm, and see which of those things you already know how to do. Are you a litigator? Did you litigate in a specific area? Does your experience move well into a specific kind of firm? Is this the kind of firm you are interested in working in going forward? Are you more of a transactional lawyer? What kind of deals did you do. I bet you are very good at dealing with interoffice politics. Never underestimate the value of someone who knows how to deal with problems as they come up and can be a good manager. Skills many lawyers lack.
If you follow up with me and tell me a little bit more about your background, I will be happy to give you some more specific advice. But in the end, I see no reason you cannot find a job in a private firm. You simply need to figure out what you bring to the table and put your best foot forward to the firm(s) you want to join.