The OP asked for "frequent bsues", so I don't know whether these count (since the whole
routes don't see the full frequency and the routes are shared between two operators, but the 52 and the 120 in Sheffield both run every four minutes.
BUT, do these meet your criteria?
The 52 is more straightforward - both operators running the same route from Hillsborough through Broomhill, the City Centre, Darnall and out to Ballifield, where they go their separate ways... then Badger Road (where they run in opposite directions) and terminate at different termini in Woodhouse. So 95% of the route sees a bus every four minutes (but with a slight difference at the eastern end). Best explained by this map:
http://www.sy-transport.co.uk/files/symap.pdf
The 120 is a different beast - during the daytime its two overlapping services with the one number. Stagecoach run Halfway - Crystal Peaks - Manor Top - City Centre - Hallamshire Hospital every eight minutes whilst First run Crystal Peaks - Manor Top - City Centre - Hallamshire Hospital - Broomhill - Fulwood every eight minutes (i.e. four minutes from Crystal Peaks to the Hallamshire, but with one common route and a co-ordinated timetable). Evenings and Sundays sees a combined service of every ten minutes to both termini though.
However, neither the 52 nor the 120 meet the "all journeys running the full length" definition that you may want to apply to this kind of thread. Still the most frequent in Yorkshire, as far I can see.
Historically, the most frequent service in Sheffield was the 52 in the early 1990s, running every three minutes with one operator (SYT) plus competing journeys run by Yorkshire Terrier, SUT, Sheffield & District (plus Sheffield Omnibus running evening/Sundays only) - i.e. five operators running the same service.