The untold part of this story makes me wonder how a very old bowl would become the target of an insect attack. Wood that is newly turned may have had an infestation of insects and sometimes they are beneath the surface and don't make their presence known for several month until they finally gnaw their way to the surface. A very old wooden bowl or anything else like wooden furniture that is indoors being attacked by insects other than termites or wood ants doesn't sound plausible. Even in the case of termites and wood ants, there needs to be a close path to moisture. Both of these insects eat from the surface inward. If the problem were either of those two insects, there would be a lot more to be concerned about than just the bowl. Maybe the bowl was being stored in a barn or some other location that made it a more inviting target. Another possibility is that it is a "new" old bowl that had some insect larvae in the wood. However the bugs might have gotten there, getting rid of them isn't easy.
From my experience of trying to kill the borers in mesquite, it seems to be mostly a futile exercise. I've tried freezing, moth balls, and various poisonous chemicals like acetone, lacquer thinner, alcohol, toluene, xylene, and MEK without success. None of these things penetrate deep enough to be worthwhile. I haven't tried cooking, but that seems to be the most likely to work. The problem is that it might also damage the bowl. Since it is too large to fit in a microwave oven, a conventional oven on its lowest setting (usually around 180° F) for about 30 minutes should kill the bugs and hopefully won't cause the bowl to crack.
