How do I convince mini bridge to open?
Mini Bridge is a panel in PS and acts as the connection between Bridge and Photoshop. Therefor you have to start Big Bridge before being able to use Mini Bridge.
However clicking on the tab of the panel (by default bottom left when having Application frame active on a Mac, don't know about Windows) should open the panel and show a button to start bridge if it is not already active.
If you have problems with this first reset the workspace in PS and if this does not work you should reset the prefs of PS (shift + cmd+ option _ on a Mac, probably Windows has contrl instead of cmd.) and choose to reset preferences.
After this prefs have been set to factory defaults so you have to reset your custom wishes again (UI color, scratch disk, tools precision etc)