I have a gold fish which we won at the fair. It's been in a goldfish bowl for about 6 weeks & is?

... thriving. We decided to buy a small tank with a pump& a new fish. We put the new fish in the tank then added our 1st gold fish. He seemed to be bullying the new fish following him & nudging him, the new fish looked scared do I removed our fish & put him back in his bowl. I don't no what the problem is as I am new to keeping fish. Please can anyone help