What is the best way to get from Chepstow to Hay-on-Wye, using public transportation?
Might be easier said than done. Looks like no trains go to Hay. Two bus companies serve that region: Stagecoach.com and Firstgroup.com. I think you should call them to see if you can do this, rather than trying to interpret their timetables.
Wild guess is that it won't work unless you get into Newport, then make your way to Hereford (England) and from there to Hay-on-Wye. Another option might be to find a way to Brecon, then catch a bus. No matter how you do it, it's bound to be an all-day project to cover the fifty miles or everwhat it is. If you drive, it's no more than a hour and a half. I've spent a lot of time in Wales (always driving) and have never stumbled across anybody that used public transportation except along the coasts. Good luck. And post the anwer if you find it.
I tried to find public transport to Hay-On-Wye and failed miserably. It's not well served, and has difficult connections to other places. I don't think there's a best way, I don't think there's an easy way. There's just the least painful or complicated...
In my experience Wales is not well searved by public transportation. Contact someone in Hay (hotel, book store) and see if they have suggestions. If there is a bus they should know
Per hay on Wye website; nearest train is Hereford (22 miles) there are busses from Hereford to Brecon via Hay on Wye (look to be about 8 per day). Timetables via the hay website. This is the only bus to Hay mentioned on this web site