Neutral and ground connected to one bus bar in subpanel; should I change?
You are correct in your assumption that your neutral and grounding conductor must be separated in subpanels per the NEC which only allows neutrals and grounds to be attached on the same bus in the Main Panel with a main circuit breaker. You or a contractor should go out and purchase a second bus and separate the conductors.

I can also say that your situation is not uncommon in the industry. This subpanel was probably installed by the pool company and whoever installed it had limited experience.

The question most people ask is, is it safe? The only answer I can give someone without a seminar, is that it is less safe the way it is and it does violate the NEC. So you have discovered it and it should be corrected.