Some thing called bash, wants access to system events. What does that mean?

The UNIX shell, whether Bash or Zsh does not ordinarily throw a dialog asking for access to system events. This is usually something that might occur with an AppleScript or Automator application while attempting to resolve runtime macOS security precautions. If this is the case, and without the code behind it, not much more can be said.

bash stands for "Bourne Again Shell", and is the old command line interpreter used by Applications -> Utilities -> Terminal.

The current macOS shell is zsh, and I do not know what the z stands for, but it is what macOS is pushing as their command line interpreter when using the Terminal.

bash is shipped and installed as part of macOS.

See the first paragraph under History for this Zsh wiki entry. Apparently, it was the login name for a professor at Princeton U and the original name source for this shell.