This is indeed the first question to ask. According to ChatGpt (don't beat me up)

>>> Yes, fish brains have a blood-brain barrier (BBB)

You can't just say "don't beat me up" and expect not to be beaten up.

Anyway there's a pdf here that probably tells what kind of a BBB zebrafish have.

https://www.mdpi.com/1422-0067/22/22/12111

And the article itself says "... communities of bacteria thriving in salmon and trout brains. Many of the microbial species have special adaptations that allow them to survive in brain tissue, as well as techniques to cross the protective blood-brain barrier."