The average fuel consumption on a full-sized bus (from the 70s to today) is around 2km/Litre. That is, for every 2kms you travel, you use around 1 Litre of Diesel (Petrol has not been used in big buses for many decades).
Bus fares in London are subsidised to the tune of nearly £1bn a year, as Stagecoach observed in your article. As it is, there are four times more bus trips than rail, which gets a subsidy of £5bn a year.
Transit buses are a LITTLE more fuel-efficient, but not as much as many people might think. A car (24.2 MPG) with the national-average of 1.5 passengers gets 36.3 PPMG (Passenger Miles per Gallon). A transit bus (3.3 MPG) with a national average load (9.1 passengers) gets 30 PPMG.
Thanks in part to these technologies, U.S. freight railroads can, on average, move one ton of freight nearly 500 miles per gallon of fuel, making rail the most fuel-efficient way to move freight over land.