First,
Thank for the creation of this tool under Linux ! Very useful !
The tool already help to target which categories of files/objects to delete, it allow to previzualize them also. But for less risk situation, it could be possible to have a checkbox to save a log result (in /var/log/bleachbit.log) when we press the "Delete" in confirmation button box... Even if the main goal fo BleachBit is to increase free space. Keep a trace of removed files can help in case of issue after the cleanup is done.
In console we can set --debug-log=[/where/i/want.log] but it's more a "debug" than just a history action.