Select the text frame (which you call the bounding box) with the Selection tool. Choose Object > Fitting > Fit Frame to Content.
And another approach, if you need your text frame remain of that width, for whatever reason...
Most likely, you have your text story (which is now selected in your screenshot) aligned right.
With text story selected, as it is now, try hitting Ctrl+Shift+L, or choose Align Left in Control or Paragraph palettes.
It does nothing when I use Object > Fitting > Fit Frame to Content