When I select an object using the direct selection tool the bounding box does not appear.
The toggle for the Bounding Box is Cmd(Ctrl)-Shift-B. This turns the BB off or on.
This would not work with a direct selection tool.
This is normal behaviour if you are actually using the Direct Selection tool.
In this case you can hold down the Cmd key (after direct selecting) to temporarily enable the bounding box.
Thanks, I got it now.