The walk starts (or ends) at the remote location of Rhyd-y-benwch which is not served by buses. You have 3 options:
Use the Severn Way to walk the 8 miles (12.9km) from (or to) Llanidloes, well served by buses which connect with the nearest railway station at Newtown.
If finishing the walk at Rhyd-y-benwch you can retrace your steps to Llangurig (12 miles/19.3km) which is on a main bus route.
Use a taxi service (or friend) to be dropped off (or collected from) Rhyd-y-Benwch. There is no phone signal at Rhyd-y-Benwch. See here for taxi details