Cambus and Premier did sort of compete between Cambridge and Royston in the late 80s. Premier had a Cambridge to Luton Airport service, which was basically A10 to Royston, A505 to Luton. It charged higher fares than the Cambus route between Cambridge and Royston, but it ran evenings and Sundays which Cambus didn't.
I don't think Royston ever had many very frequent bus services. In that era, the only ones that come to mind as operating more than about twice a day were the 797 to London via Hitchin, the 798 to London via Buntingford (both Green Line with some journeys run by Cambus), the Cambridge route, and the Bassingbourn route. I think Cambus and Premier may both have had that one at different times, but I do remember once taking a Luton & District bus from Letchworth to Steeple Morden, and connecting there with a Cambus double decker to Royston.
As for NBC days, from what I remember, the peak hours trips to places like Barkway, Chrishall, and Newport Grammar School were run by Premier. I'm not sure who had the market day runs to Bishop's Stortford via lots of villages, and Saffron Walden via even more villages. I don't think H V Richmond (Barley) was doing service bus work yet, Elsie Smith (Buntingford) was but only went to Hitchin, so those too may have been Premier.
The trip down the A10 to Buntingford only ran Wednesdays and Saturdays in those days. That was United Counties 188, starting from Biggleswade.