In my experience the timings come from many sources. The bus company themselves, the company who arranges the bus provision or the TOC, based on their own efforts at timing. In olden days it used to be a man in a Viva Van who was instructed not to go above 30mph! I have known one planner get his preserved bus out to do the timings.
The filter of a middle man between the actual bus company and the railway planners is, in my view, a regrettable one because any local company really knows the traffic conditions. When I was planning replacement services, their ability to say, no, you need to allow for the Sunday Market at X or a sports event at Y was invaluable.
As an aside, the only thing that used to infuriate me was many of the good local firms were so rubbish at billing. How they stayed solvent or paid their drivers beat me. I had to threaten one that I would send my finance team in to do his billing if he didn’t sort it out himself! He was that good for us, I didn’t want him to go under.
If I was doing it now, I would have less choice of operator in that part of the country and I would probably be forced to use the middle men too.