1. Check Units Setting
First check that your settings are correct by typing DDUNITS, adjusting to your liking, and also hitting the Direction... button to ensure this is set to North.
2. Type < When Entering a Bearing
Then (and I found this quite confusing at first), in order to enter bearings from north you don't hit tab and enter them in the box shown here:

Instead you need to type the < character and then the bearing, so it looks like this:

You can enter the distance first or the bearing first, I don't think it matters, as long as you type the < before the bearing.
Couldn't find that clearly explained in the manual anywhere. Crazy.
3. DYNMODE Setting
I later discovered that you can type DYNMODE 1 in the AutoCAD command line and it will then show the correct bearing from north when you're drawing lines, not the angle from east.
According to AutoCAD this disables the "Dynamic Dimensional Input" feature, which is actually just getting in the way.