The bus that appears in the ITV 1 programme is Bristol LH registration OCA629P which was ex Crosville acquired by The National Coal Board. The Coal Board then sold the bus after the miners strike and it was purchased by Trimdon Motor Services. OCA629P ended up with Tees and District with fleet number 1934 before going for scrap in 1994.
My recollection is that when miners started returning to work buses were provided in house by NCB or from small coach operators and or small security firms. The major operators (National Bus Company) only resumed their miners contracts near the end of the strike when numbers returning to work and increased police presence made it feasible.
EDIT: The programme that I watched was on ITV 1 at 10.35 on Wednesday 12th March titled "The Miners Strike and Me". I assume that the programme will be available on ITV player.