If there is truly a bone lodged in your dog's throat and you can not see it to remove it, then the dog will need to see a vet. If your dog ingested a bone, it may have scratched the throat going down and is causing coughing and gagging. You can give your dog a piece of bread that may wrap itself around the bone and allow it to go through the system easier. You will need to keep an eye on your dog’s stools to see if the bone passes through your dogs system as well as for signs of fresh blood or mucus.
Fresh blood or mucus indicates inflammation within the large intestine while dark black or tarry looking stools indicate bleeding in the stomach or small intestines. If your dog’s stools become black then your dog should see a Vet immediately. If your dog begins to vomit, has a lot of diarrhea, becomes unresponsive to you or squats without having a bowel movement then you should take her to the vet immediately as well. As long as your dog is acting normally just monitor your dog closely to be sure the bone passes through your dog's system.
In addition, bones can splinter and puncture the gastrointestinal tract causing peritonitis.
If you didn't see the dog actually eat a bone but are basing your statement on his gagging, he might be coughing. Coughing can be caused by upper respiratory illnesses, collapsing trachea and heart issues. Kennel cough is normally contracted when a dog has been boarded or kenneled or around a large number of dogs such as at a dog show, dog park or pet store. Here is a website with more information on kennel cough. http://www.thepetcenter.com/gen/kenc.html
Canine influenza is now becoming more prevalent and like it sounds it is a canine flu. Here is an excellent site on it.
You will want to monitor your dogs condition looking for colored discharge from the nose or eyes, a productive cough (coughs stuff up), stops eating or lethargy. These are signs of a possible bacterial infection as well and my require antibiotics. If your dog appears to be having a difficult time breathing, you will need to see your Vet as some dogs dog get really sick with canine influenza and need support to recover.
To help your dog breathe easier you can run a NON-medicated humidifier in the room your dog is in, or sit in a steamed up bathroom with your dog to help keep the mucous moving. Robitussin DM at a 1/4 teaspoon per 5 pounds can be used to control the cough. Dosages can be obtained at this website. http://www.petplace.com/drug-library/dextromethorphan-robitussin-dm/page1.aspx
There are other reasons for coughs such as heart problems which should be investigated if your dog is not on heartworm preventative or is an older dog. The following site goes over canine coughs.
Your dog could be doing what is called a reverse sneeze or a collapsing trachea. Here is a site on reverse sneezes and one on collapsing tracheas.
I hope you find this information helpful.