Tell us about yourself!
The answer to your question is to continue to orient the lines in your housing to the grid lines on the map. The black north arrow you refer to is called an "orienteering arrow". Think of it this way; when sketching a bearing on the map, ignore the magnetic needle and the black (red on many compasses) arrow. You can sketch a bearing upside down if you wanted. This is because you are using your compass as a protractor. You don't need to orient the map to sketch a bearing. This is your "true" bearing or "grid bearing". Now when you put your map away and box the magnetic needle inside of the orienteering arrow, you are headed in the right bearing. Hopefully this info helps whoever comes across it.
Keep in mind that you don't have to orient your map before taking a bearing.