Opening photo file from Bridge into Photo AI allows for all the options including up-scaling (what is great), but you have the only option to save it to Bridge again what OVERWRITES ORIGINAL FILE - WHAT IS WRONG!
It should work like in case of opening from Explorer what let’s you to chose place and name of saving file, including additions of parameters used.
In the export settings, you can choose to disable overwriting. You can also add suffixes and prefixes to save as a different file. Let me know if that works.