Get a bright light and look at him carefully. Make sure he doesn't have anything growing on him you can't see with just the regular tank light.
You can check for velvet this way which may be a good idea - just in case. velvet would look like the fish was sprinkled in gold dust but if he is acting normally, eating and not clamped - I think he is just fin nibbing.
I had a blue halfmoon that was a chronic bitter till the day he died. Aparently he wanted to be a CT and not a HM >.<
Did anything in his tank change before he started bitting? More decorations may help if he is stressed or bored
if you do use bettafix, be careful with it and do not OD on it - too much can destory the organ they use to breathe with