We say the best way to wash your pack is simply with water and if needed, a pressure washer. You can either rub the dirt off with your hands or else you can scrub the pack with a soft brush. You should be able to get most of the dirt off this way.
If you feel that you need to use soap, use a mild or pure soap and rinse the pack thoroughly to remove any residue. Hang the bag to dry (don't use a dryer or any other source of heat). If you hang the pack outside, leave it in the shade. It should dry overnight, but it might take longer depending on the climate.