So I did this today and can leave some information for anyone else considering it.

I took to 308 down to the Green Man coffeehouse (former pub). It's the closest stop. It's an Arriva bus so the Arriva 133 took my return ticket from the Four Ashes stop.

The Green Man is right by the Flitch Way path. There's an interesting information placard by the rail halt and an interesting rail bridge there. But I don't recommend entering the forest by the entrances off the Flitch Way unless you're wearing wellies. the horses make those paths total mud baths.

Instead it looks like walking down parsonage road to the main entrance lets you access the much less muddy hard gravel paths and boardwalk.