While I think that this a very subjective question, I believe that you can get an indication of from the doctor's experience and number of cases the he/she has done.
You must also feel comfortable with the surgeon you pick, so that you will trust the decisions he/she makes for you.
Almost every orthopaedic surgeon will know how to do a standard “open” bunion correction. However, the thing that will differentiate a particular surgeon from the rest would be if he/she can suggest (and perform) other ways of surgical correction that might be more suitable for the patient.
Take for example a keyhole / minimally invasive surgery (MIS) for bunion correction. Most patients have mild to moderate bunions, and that is most suitable for MIS corrective surgery. The are more advantages to performing MIS, such as reduced bleeding and risks of infection.
However, a MIS takes highly specialized skills and training, and it is a steep learning curve. There's only a handful of surgeons who are able to perform this type of surgery.
So, before you agree to getting a bunion correction done, it would be useful to seek a second opinion on whether MIS/ keyhole surgery would be a better alternative. And if your foot is suitable, there is absolutely no reason to get the correction done via the open method.