Goldfish do try to bully one another to establish something like a pecking order in their tanks. Usually, in time they get along but this is easier to accomplish in a large tanks with lots of hiding spots, so each fish feeling bullied has a place to hide and escape the harassment.
If your tank is too small chances are the bubble eye goldfish has nowhere to run to in order to escape the bullying. If your tank is big enough you should add in lots of plants and decor so that he can hide. Add in large plants like Java Ferns and Anubias Nanas as goldfish will simply eat the smaller plants (they also attempt to eat larger plants FYI). Decor is actually very tricky to pull of with Bubble eye goldfish since anything remotely sharp will just be horrible for them. I would stick to the plants.
But the solution is to separate them. Goldfish do okay short term in low tropical temperatures, but they aren't compatible with any other species of fish long term and should be either housed alone or in a species only tank. If your tropical tank has any sharp decor or gravel this will spell disaster for the bubble eye goldfish. Not to mention, they aren't particularly fast at getting their food, the other fish might easily out compete him for food and eat all of it before he even finds out it's there. Fancy goldfish aren't particularly strong swimmers and sometimes lack good vision to see food quickly. They almost always rely on smell to find their food.
Keeping a goldfish alone doesn't stress them. They are social fish, not shoaling fish. They may prefer the company of more of their kind, but they do fine (and sometimes prefer, like you've seen) if kept alone.