I suspect that no one has replied to your post as nobody can think of a site, on a bus route to the Freeman.
There is the Old Hartley Caravan Club Site near Whitley Bay, you would then have to get (probably) a bus, a metro then another bus.
I can't find any suitable CLs or CSs.
There is a site at Rowlands Gill - Derwent Park Caravan and Camping Site (01207 543383), again two buses required to get to the hospital.
Good luck in your search.
Steve G.