Thanks so much for the answers to my questions.
Gum color is normal which is good as is the fact that he's otherwise acting fine.
It would be somewhat unusual for a bone to cause intermittent bloody stools for this length of time with no other symptoms of obstruction although I suppose it's possible.
Of course, an x-ray of his intestines would immediately confirm whether or not this is the problem since a bone would be visible.
And, while seeing blood/mucous in stool can be alarming, it doesn't necessarily have to be concerning since there are numerous other possible causes for it including internal parasites or inflammatory bowel disease, for example.
If this were my case and you didn't want to have an x-ray done (for whatever reason) and since he's otherwise acting fine, then I'd treat him symptomatically for a few days to see if there's improvement. If not, then additional tests (including a fecal sample in addition to intestinal x-rays) might be prudent.
The following would be my suggestions:
1. Feed a bland diet of 1 part boiled chicken (or hamburg) to 4 parts 20-minute white rice. Feed only a small amount of one time, 3-4 times through the day. I would not feed any regular dog food.
2. If he is not currently taking any aspirin or nsaid products and since he is not vomiting, then you can give Regular Strength Pepto Bismol. The dose would be 1/2 ml/lb 2 times a day. For example, if he weighs 50 lbs, then you would give him 1.5 tbs at each dose (15 mls=1 tbs). It may change the stool color to a gray-black or greenish color though so this shouldn't concern you if it happens.
Pepto bismol should not be given to vomiting dogssince it contains salicylates (the active ingredient in Aspirin) which can irritate the stomach.
3.Consider probiotics such as Forti-flora.These may be available at local pet/grain stores.
If he had perforated his intestines, he would be a very sick dog since peritonitis would develop very quickly, so I think this is less likely. However, if a portion of the venison bone has become lodged in his intestines, then there might be sufficient irritation to cause the blood which you're seeing. If it were still in his stomach and causing irritation, then dark blood (melena) might be seen.
Either way, if this is the problem, then surgery is more than likely going to be needed to remove the bone since it would not appear that he's going to pass it unfortunately.
However, let's hope that the bone isn't the issue and that perhaps something more innocuous such as parasites or IBD are the cause of his symptoms.