How big of a bone do you think he swallowed?

Is he acting normal? Drinking and eating normal? If he's acting normal, I'd just keep an eye on him. If he becomes lethargic, doesn't drink or eat properly or doesn't seem to be passing stools like usual, I'd take him to the vet.

Of course, you can't be too safe so a vet check may be in order if you'd prefer.

When Kai ate a bone, I took him to the vet. Just told me to keep an eye on him.