This sort of thing is extremely common with running- I've had many experiences running for the woods on longer more strenuous runs. I've never had bleeding, but I know other people who have.

That said, there are a number of other problems that can cause blood in the stool and it's a very good idea to get checked out to make sure there isn't something more serious going on.

I'm confused though- are you saying your problems start before you are actually running? This might imply something else is going on as well. Before races my nerves get going and I'm in the bathroom several times (I actually find it kind of useful to empty out), but in general you can't blame the running entirely if it starts before you run. Irritable bowel could make you need to go more frequently but it shouldn't cause bleeding. There are some other colon conditions (Crohn's, ulcerative colitis etc) that could do this as well.

If we assume you get checked out and everything is okay and it's just related to running- here's what's worked in marathons for me:
-Hydration
-Salt tablets (I'm currently using lava salts)
-Pepto- bismol (I've known other people who use Immodium, but Pepto seems to work better for me)
-Avoid fiber (salad etc) the night before

Basically on an intense run, most of the available blood flow is going to the legs. The colon isn't getting it's share and it gets irritable (or in some cases down-right angry). Avoidance of dehydration will help keep from aggravating the problem.

I hope everything works out okay!