Newbury buses were always a section of Reading buses/Transport I thought. As the latter, they are now sharing Routes with Newbury and District (Weaveaway) and in fact as mentioned in another thread are contracting Weaveaway on their Jet Black route.
I think you're right, and Bee Line were in between the two, though Bee Line were a privatised and re-branded Alder Valley
being as im only 30 years old the only buses here i remember are the yellow bee-line buses, i can remember seeing them around newbury when i was about 5 or 6