Ctrl+H is for Hide Edges
What you want is Ctrl+Shift+B or View → Show Bounding Box.
Note that in order to see the Bounding Box you need to be using the Selection Tool (V).
You can also hold down Ctrl while most other tools are active to quickly switch to the Selection Tool.
In your case, it seems that all your paths are in a clipping mask – you can release it via Right Click → Release Clipping Mask or Ctrl+Alt+7.