Well, ants don't eat wood...so I doubt you have ants...you might have termites.
Ants would have to come out and forage for food.

You'll have to find an exterminator that can "bag" the table and use a gas type fumigant to rid the table of what is probably carpenter beetles.
Termites possibly but you'd most likely have to see small tunnels made by the termites to protect themselves from the elements as they traverse back and forth to their native home in the soil. Effectively, no access to other areas of the soil or house would eliminate that critter.

Check the outside of your home around the foundation and in your garage for mud tunnels. Termites are ant like creatures at one stage of their life and they usually swarm. I don't know if they eat wood then or not. Look for bubbly spots on your walls or paneling that looks strange. We have had termites at every home we lived in. This is a new home and had it pretreated before I moved in.