The closest bus stop the Mountain Centre is located within the small village of Libanus. From the bus stop, it is still a walk of about half an hour to the Mountain Centre itself.
I went to the Brecon Beacons by a bus of the Sixty-Sixty bus company, but unfortunately this connection was cancelled in the end of March 2012.
Now the best option (as far as I can see!) to get there from Cardiff is by Stagecoach bus, they leave Cardiff from monday to tuesday at 08.20am, 10.20am, and from then on roughly every two hours. As these times are exactly the times of the former Sixty-Sixty connection, I assume that they have just taken over their services. Stagecoach does the reverse journey - from Libanus to Cardiff - every two hours as well.
Libanus is one stop before Brecon. No matter if you go there from Cardiff or from Brecon, you should advise the driver that you want to get off in Libanus, as it might be an "on request" stop. If you are waiting at the bus stop, in any case wave at the driver to make sure the bus stops.
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Don't know if you have heard of Beacons Bus, it is a Sunday Bus service that runs to all sorts of places in and out of the National Park, Brecon is the hub, so all the early morning buses make their way to Brecon arriving at 11ish and then go out again on various tours, you can get all the way to Carmarthen and back if you really want to. Any how we have got paper copies of the timetable in the office or you can see it online at www.travelbreconbeacons.info There is even one bus with a bike trailer, it starts on Sunday 24th May and runs every Sunday and Bank Holiday Monday until the 27th September.