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The best spot is Vigo footcrossing which is off Alcester Road in Burcot. Can't help with public transport. Other decent spot is the fields off Pikes Pool Lane.
There was certainly a foot crossing there two or three weeks ago. If you click on the location if you go the Flickr page of the photo below, my camera has a GPS log and the map will show exactly where I was standing when I took the shot.
Or join the Scouts and go camping at Blackwell Court; did this in summer 1980 - ten days camped literally just below the summit and in those days it was mostly 45s thundering up the incline on passengers ( 37s on freights )...
Any time I go there I get a train to Bromsgrove and walk. For me takes somewhere under 30 minutes, a more-less simple straight route as you follow the course of the line. Naturally, most of it is uphill, but easier coming back. I found the route on Google Maps by just following the road that goes beside the line.