Well I was playing just now and when I was fast travelling it told me that when that weapon has that green arrow icon on it, "it may be better than the one I have currently equipped". You guys said it's poisoned, I tried firing it. The icon is still there. So technically I haven't used the poison.
Items that are better than the one you have equipped have a white/greyed-out white (meaning, the same color as the text next to them) triangle (not arrow) to the right (not left) of their name in your list of inventory items. When you hover your mouse/cursor over an item in that list, the item's description is displayed in the main portion of the screen on the right. In that description box, a green arrow with a green snake around it, in the top left of the box, indicates that the weapon is poisoned. Once you use it, the poison is used - for a melee weapon, you need to make a successful hit, but with a bow, since the arrow is poisoned, even a missed shot uses the poisoned arrow. I just tested this to be sure, and even in God Mode (on PC) the bow loses the poison icon after firing it. I imagine you have a bug if your weapon is remaining poisoned after use.