So this is a simple trick. The in-game timer is saved on contact with a bell. By exiting to the Main Menu and then Continuing, you will be restored at your last bell with your in-game time set back to the previously saved time.

This means you can redo a section of the run over (from the last bell) with no time penalty.

The rules don't mention this trick. I'm guessing this is not allowed though.

Side note: This trick makes it possible to do password storage glitch within a single run, without any in-game time lose.

Edit:
Forgot to mention that dying and respawning at a bell does not count as hitting the bell, so the last save will not be affected. meaning exiting and continuing will still work.

That's technically a segmented run instead of a single segment, so no it wouldn't be allowed.

Yeah thought that'd be the case.