Darren from Hak5 is touring across America to hacker spaces and the like, and he did something like that[0] which surprisingly was used to power more than I thought would be feasible. And this was on a sprinter van, so with a bus like this, one could get 4x the amount of energy.
Sample window air conditioner: http://www.sears.com/kenmore-15-100-btu-room-air-conditioner...
1410 watts, AKA 2 horsepower.
Old fashioned space heater: http://www.sears.com/kenmore-oil-filled-indoor-heater/p-0327...
1350 watts
That being said, I feel like one would probably better off trying to solve the heater on the cold night problem by first approaching it from a fluid dynamics perspective (kind of like a glycol HVAC) and then using minimum energy for things like a pump. Though that is probably outside of the scope for this specific project, but it is probably worth looking into for those interested in building on what is going on here.
If one of those units is enough for the bus, and it's on 30% of the time that would mean around 250 W per hour power requirement, resulting in 6 kWh over the day.
In a reasonably sunny environment, solar panels can get 100 W per square meter. Let's say there are around 15 sqm available on the roof, yielding a total of about 12 kWh over the day - that's assuming around 8 hours of sun. If that doesn't work out due to latitude, it would be relatively easy to design panels that can be unfolded, providing extra area and serving as an extensible roof at the same time.
If batteries and inverter don't swallow more than 50% of that yield, it should be enough to drive a normal AC, lighting, and a laptop, maybe even a small fridge. You'd need a backup stove for the winter though.
This is why some full time RV'ers are picky about what state they are in for a given season. If you're in Texas, or another hot climate in the summer in a large bus, you'll need two or three tons (24,000 to 36,000 BTU) of A/C capacity (sometimes more!) to keep it habitable through mid-day and late afternoon.
If you have a large (cover the roof) solar/battery/inverter system, you can run all night without having generators start (and interrupt everyone's sleep) in most cases.
Most people that I know of use LP for heat.
Many of the comments here about cooking fuels being heavier than air are correct about the danger- nothing that proper ducting and a bilge pump could not handle. In order to live like this you must adopt a camping lifestyle. Everyday life activities, such as cooking and bathing, become more like camping and require more preparation.
edit-poor formatting, sorry. I meant the asterisks to be bullet points.
Natural gas would be ideal, gasoline in a good engine second best.