How big of a hole? That is going to help make a decision.
They have longer length drill bits at home depot, I have a few in my toolbox at work, I think they are 16" long but I could be mistaken. They may be longer, you can try there, but I think they only go to 3/8".
You could get an auger bit that is long enough to go from both ends and meet in the middle. But it's gonna' be pretty expensive and a pretty large hole.
Maybe you can tack weld a bit to a peice of threaded rod.
If it's big enough for a spade bit (at least 1/2") they make extensions for them but you're odds of drilling straight are not so good. Unless you use a drill press and start with the bit only and add one peice of extension at a time. Still it could run off on you, but if you're turning the peice over and only doing 18" at a time it might work out for you.
The same goes for hole saws. I have had six feet worth of extensions on a hole saw before, but that was to drill an electrical access hole thru horizontal plywood ribs in a preexisting panel.