You can take a train from Cardiff to Newtown via Shrewsbury in around 3 h 36 min. Alternatively, Stagecoach South operates a bus from Cardiff to Newtown 5 times a day. Tickets cost $32 and the journey takes 3 h 43 min.
From Cardiff Central train to Shrewsbury then train to Newtown (Powys). 3 h 36 min £51. From Cardiff, Castle Stop KA (Cardiff Castle) bus to Newtown, Ladywell House. 3 h 43 min £22. From Cardiff drive to Newtown. 2 h 2 min £17.