If you haven't noticed, you occasionally find arrows in your inventory if you get shot through with some. I would suggest trying the guards method, and even go as far as 'taking an arrow to the knee' in the wilds. Elven arrows are a waste of time to 'dupe' as they're near impossible to find on the ground. I have a bountiful supply of ebony arrows at only level 12, and an extensive supply of dwarf, orc, and glass.
However, with everyone's statement about deadric arrows being shot from guards in cities or your housecarl are actually true. From what everyone has stated, the dawngaurd expansion gives you that ability.