What sort of bone? A dog that is allergic to beef, for example, is going to be allergic to all parts of beef, including the bones. But the same dog - if it does not have an allergy to chicken, is not likely to be allergic to chicken bones. It is the type of animal the bone came from that counts, not the fact of consuming bone, per se.
It is, however, possible that a dog might have a sensitivity (i.e. intolerance, not allergy) to things such as the marrow in bones of all types. But that would arise from - for example - not tolerating the high levels of fat in bone marrow very well. Food intolerance is a different thing to allergies, but can still produce effects - for example, tummy upsets (nausea, vomitting). What you would not see though, is typical allergy symptoms such as itchy skin, ear infections, etc. Nonetheless, food intolerances do make the dog feel unwell, so the answer is similar to allergies - that is, things the dog is intolerant to need to be eliminated or very restricted in the diet. With bones, one might in that case take care to feed only bones that don't have large amounts of marrow in them, or to substitute cartillage or even crushed eggshells instead.
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