Bugs like you saw holes from are probably powder post beetles. They love ash, they love it alot! Hickory is also another one they like. If you bring the wood in and burn it right away within a day or so you will be fine. These and many other species of beetles taste the wood they lay their eggs on and so in a house that has polyurethan, stain, paint and all manner of other surfaces covering the wood they will not find a suitable taste to their liking and they will not lay eggs. Once the eggs hatch very tiny larvae tunnel into the wood, usually into the bark and cambium layer and that is where they feed until they are ready to metamorphose and come out as a beetle. Your house is very safe because they prefer bark to almost anything for laying eggs on.
Any tree in a woods or in a wood pile has tons of bugs and critters on it that you cannot see, and if you limit your selection criteria to just what you can see you are missing 90% of the other critters. So burn them all, as someone else said, they are all BTUs.