Hello Organic Shoes,
I cannot say whether any day tours will coincide with your visit to Cardiff. Bit of a long shot, I'd say. Otherwise you get to Hay-on-wye from Cardiff via either Brecon (bus, bus) or Hereford (train, bus). Can't say which is quicker door-to-door, but the bus interchange in Brecon is 2 minutes from the centre of town with much to offer if you have to wait for your connection. Hereford train station is a mile or so from its centre. If you're really keen though, you could get an early train to Abergavenny and pick up the Offa's Dyke footpath to Hay, about 20 miles distant, via Capel-y-Ffin, Llanthony and Hay Bluff! Given the travel time by public transport you may wish to consider an overnight stay in Hay-on Wye. On my last visit I stayed at Rest For The Tired B&B. Really comfortable, welcoming hosts, and a good breakfast. It's above one of the bookshops. Plenty of others too of course. Enjoy your trip.
Further to my last post to this thread. From Cardiff to Brecon is by coach, route T4.
Thanks so much for the information!
The quickest route according to http://www.traveline-cymru.info/ for a random Wednesday in September appears to be train to either Abergavenny or Herford and then the bus. Bus and coach only options take 3.5 hours.