(Universal private eye series, 1980-8)

Episode 1.18: Beauty Knows No Pain:
Hawaii-based private eye Thomas Magnum (Tom Selleck) is best known for his Ferrari, but in this episode he rides the bus with guest star comedian Marcia Wallace. The bus in question is TheBus 260, a AM General Metropolitan 10240 new in 1975:

Episode 2.05: Memories are Forever:
Opens with clips of Vietnam, including this, taken from the feature film 'Apocalypse Now':

A street scene includes a glimpse of another TheBus AM General Metropolitan:

Episode: 3.06: Black on White
Opens with scenes set in London, but unsurprisingly shot in Hawaii. An AEC Regent III/Weymann lowbridger from London Transport's RLH class passes the camera. Four were exported to Hawaii:RLH26, RLH33, RLH36 and RLH47; RLH47 suffered damage from a falling tree in 1982, so can likely be excluded, but this one is not identifiable:

Episode: 3.22: Faith and Begorrah:
American TV has made some strange attempts at representing Britain and Ireland, and this might be the strangest. The episode opens with a party of tourists visiting a tiny church in Armagh, Northern Ireland. However, the hills in the background look a bit pointy for Ireland, and the bus is 140HUO, a former Western National Bristol Lodekka FLF with the fleetname 'Windsor Tours', but actually owned by Windjammer Tours of Hawaii!

(thanks to Noel Baxendale for this sighting)

Episode 4.02: Luther Gillis: File #521:
A woman being chased makes her escape on TheBus 255, another 1975 AM General Metropolitan 10240:

Episode 4.11: Jororo Farewell:
Features an International Harvester S-series school bus:

Episode 5.07: Blind Justice:
Magnum on a bus again, this time TheBus 172, a 1974 Flxible 53102 New Look:

Episode 6.01 and 6.02: Deja Vu
A double episode first aired in 1986 that brings Higgins (John Hillerman) and Thomas Magnum (Tom Selleck) to England inevitably (again) has views of London buses!
T-class Leyland Titan crossing Tower Bridge:
The Routemasters, one distant, the other RM409 (WLT409) on route 1, are to be expected:

Less so is the DMS-class Daimler Fleetline that obstructs Magnum as he chases a man through the Covent Garden area, an example with the short-lived but attractive white stripe:

There is also a glimpse of the London Transport Museum as it was then:

Plenty of cartoon English people on display, among them characters played by Julian Glover, Peter Davison and Arthur English, bless 'im. The episode is worth catching for the sight of Higgins driving a Reliant Rialto three wheeler.

Episode 7.01: LA:
Not clearly seen is this Los Angeles Metro GM New Look:

Episode 7:21: Limbo:
In the background of Magnum's Ferrari we see TheBus 975, a 1983 Gillig Phantom, with another from the same batch behind: