Speak to the count in Leywain and he will offer you 100 gold for each black bow you bring him. Funnily enough the black bow bandits are in Rockmilk Cave

You can normally find 15+ black bows in their so that's 1500 extra on top of what you sell per visit. I think you have to do a quest or two for him before he tells you about the black bow bandits and offers you the money per bow?
Fighting in the Arena is OK for money although you'll only get small amounts until you become more advanced. As champion you'll get over 1000 gold per win, but you can only fight once a week :-/