When I think of Coccidiosis, I think of younger cattle. Lots of times it's cattle moved to infected pastures. If this older cow hasn't been moved to a new pasture or new cattle brought into the pasture she was in, I would look for other reasons. Not saying it wasn't coccidiosis, but it's kinda unusual in older cattle.
From what you said about the blood coming from the rear end and no signs of being sick, I think you might have guessed right when you figured it might have been calf related.
