Paul, to do this I created a line shapefile. You can then edit and create new feature with it. As you draw a line, the distance and bearing will be shown. You can also us it to draw a line over an existing line of unknown bearing to get its bearing.
Thanks for your reply. It sounds easy but I am not seeing what you are seeing. I tried adjusting the settings under Customize> Arc Map Settings, but without success. I need more information to figure this out.
1) Where on your screen is the distance and bearing being shown? In the lower right hand corner?
2) What version are you using? ( I am using ArcMap version 10.8.1.)
3) What license level are you at? Basic, standard or advanced?