I have the same problem on any run longer than 6-7 miles. I tried using body glide and that didn't help me at all. So far the best thing I've found is 3M Micropore medical tape. I just tear off a small piece, tear that in half again so I have two little pieces (maybe 3/8 to 1/2" square) and apply. The squares are small enough to only cover the nipple and not get too much into the hairly area and it sticks well. I carry some in my water bottle pack in case I forget to put it on before and the one day I remembered after I had run 2 -3 miles and was quite sweaty already. The tape still stuck fine. It doesn't feel the best coming off, but it's not bad and sure as hell beats chaffed nips! My roll was many years old and I just ran out, so I hope they still make the stuff. If you used it just for this purpose, a roll would last a very, very long time.
Yes, I have had bleeders before and was shocked when I took off my shirt and saw the blood on the shirt. I did not realize that they were bleeding until I took off my shirt, I don't normally look down and check out my nipples while running. Once in a while they get painful while I running more than 3 miles, but lately I have had no problems with them. I like Dukes suggestion 3M Micropore medical tape. Also I noticed that the cold makes them more sensitive.
My husband used some kind of spray before he applied the medical tape around his wound (he impaled himself on his bike). I can't remember what its called, but its makes taking the tape off less painful. Some sort of no-stick medical spray.
I just got my new BFR Tech long sleeve shirt and is very light weight. I ran 3.5 miles and it seems to be nipple friendly. I believe part of the problem when getting sore nipples is the type of material rubbing against them; I have some shirts that feel like sand paper and is very painful.