I'm wondering how much time does a patient have to wait for an operation on a fractured fibula?

See an orthopaedist: See an orthopaedic surgeon who cares for trauma. She or he can assess you and give you the options. Depending on your exact condition, surgery may or may not be necessary. If surgery is suggested, it is best done shortly after the accident (unless delayed by swelling, skin problems, other injuries/issues) since the healing starts immediately. Waiting too long make the surgery harder.