As you may already know the concern is the bone causing an obstruction or perforation of the intestinal tract. But, more often than not dogs are able to digest the bone or pass it in the feces without any problem. Inducing vomiting is not indicated as the bone can damage the esophagus on the way out. This is what you can do:
1- Do not give things like Pepto Bismol.
2- Do not induce vomiting.
3- Change his diet for the next 2-3 days to rice (75%) with boiled boneless chicken or ground beef (25%). Or, add some canned pumpkin to his food every time you feed him for the next few days. The idea is for the rice or pumpkin to help move the bone out in the feces if undigested while protecting the intestinal tract.
4- If during the next few days you see the following symptoms: lethargy, anorexia, vomiting, constipated or diarrhea, abdominal pain or swelling, etc. follow up immediately with a veterinarian. These are all signs of a possible obstruction or perforation of the intestinal tract. In the meantime, observe him and change his diet as above then wean him back into his regular diet.
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Dr. Peter