Bus
T4 - The TrawsCymru T4 service is your direct link between Cardiff and Newtown.
X47 - The Celtic Travel bus from Llandrindod Wells - Llanidloes via Rhayder.
The Argoed Mill stop will get you very close on both of the above routes.
Train
The Arriva trains Wales 'Heart of Wales' line runs from Shrewsbury to Swansea. The service will take you to the local Spa Town of Llandrindod Wells where there are regular bus connections.