I have had a goldfish for over 2 years now and he is really starting to out grow her tank, unfortunately I can't get another tank because my mother will not allow it. So I'll be releasing her into a pond with some other goldfish. I used to keep her in a heated tank because I only had one at the time, now that I have a tank devoted to cold water fish she was a lot more lively and grew really fast. You are just stunting your goldfish's growth and potentially causing harm to both your fish if you let them be tank mates for too long.
Gold fish poop like none other and that requires quite a bit of water changes they also need quite a bit of flow in the tank to be happy while your betta would prefer to be in a low flow area. They are just the complete opposite ends of the spectrum as far as fresh water fish go.