Interesting thread! And some even more interesting interpretations of cowboy - some seem to imply that pretty much any independent operator is a cowboy
I wouldn't really class the likes of GHA Coaches, Western Greyhound and Hulley's (and others) as your typical cowboy operators. They're more like well intentioned, well respected operators who then grew too large and/or too quickly to maintain their standards - it becomes much harder to be "picky" when recruiting staff, much harder to be "picky" when purchasing new (to the fleet, usually not brand new) vehicles, much harder for the existing small management team to have a good eyes and hands on grasp of the whole day to day operation.
Then there were the shabby but well intentioned operators. Usually reasonably well maintained vehicles (mechanically if not cosmetically), often "getting on a bit". The sort that would run either Merc minibuses or big old coaches or double deckers - normally operating council tendered services - interworking with school services. Often rural work of the once a day each way, one day a week/market days only type services. Very well intentioned but often on a very low budget - probably no driver uniform, difficult to find service information, handwritten destinations displays - but very much operating in good faith, very friendly drivers who would often know most of their regulars by name.
The true cowboys, I would suggest, are/were something else entirely. The sort who would almost exclusively operate 7 til 7 (at best), paralleling the "big" operators best performing routes (or even the best performing sections of the best performing routes), where service information and timetables were hard to find and/or completely fictional anyway. The type where you'd quite possibly be charged a different price every time you boarded, 50/50 if you actually get a ticket. Often rude/aggressive drivers, poor driving standards. Very little interest in actually providing any sort of useful service. The kind to be seen having regular run ins with VOSA/Traffic Commissioners regarding financial standing, vehicle maintenance and timetable compliance.