Is there a way to use regex expressions to auto-fill filenames in bash?

The feature you are looking for is there. You are just missing a * in your example. Type cat file000[1-3]*ESC* and it should work. I think this is the case because the readline function insert-completions (which is bound to ESC*) will not expand the glob pattern if it does not match any files. And without the last * it does not match the files.

You can read about this in the man page, section "EXPANSION" subsection "Pathname Expansion".