For the purposes of this post, I'm comparing bus travel to driving, since bicycles have been arbitarily banned by the Leaders of the Glorious Republic, or something.
Table 10 gives 115.8g CO2 per passenger kilometer for non-London local bus, so better than nearly all single-occupancy cars, stating:
(Working backwards from a random source suggesting busses emit 1.3kg/km - that'd suggest an average occupancy of somewhere around 11 people, which sounds reasonable.)
"The factor for local buses was calculated based on data publically available from the major bus service operators including Stagecoach, First Goup, Arriva, National Express, Go-Ahead and from Transport for London, supplemented in some cases by average bus occupancy factors from national statistics."
However, accounting for bus CO2 emissions by average occupancy does get complicated when the assumption of average occupancy is not true. For example it'd lead to the counter-factual notion that it'd be more environmentally friendly for fifty people to pair up and drive 25 cars
from A to B than to all pile onto the same bus.
Thinking about what this accountancy means for individual actions; would two people going to the same destination would be more environmentally efficient to drive or take the bus? If enough people chose to make that journey, it'd be much more efficient than driving; if enough people chose _not_ to make the journey, it might (depending on their other transport choices) be more efficient as the bus wouldn't run at all. That means there's an environmental minimum for bus travel at the point that a bus service is only just financially worth running for the operator, which probably means many subsidised bus services are harming the environment.
For regular trips, I am obviously part of the average occupancy (or all people in my group are), and should simply divide the average number of people on the bus for my trip by the bus' emissions per kilometer (which I imagine I could in theory get from the manufacturer or operator or somebody), and compare with driving.
For ad-hoc travel, I can probably discount my influence on average occupancy. That appears to mean for such trips, I should avoid busses that are on average poorly utilised, and choose to use busses that are well utilised. For a small group (≤ 1 car load), the more people I have with me on the trip, the better utilised the bus route already needs to be in order to mean it's more efficient than driving. Given that DEFRA say the data is publically available, and it's meaningful, it should be better publicised.