If you have an alternator like the Delco 50DN, it will deliver around 270 amps at 28 volts, for a power output of 7500 watts. That's at full wack, but pulling 3500 to 4000 watts is no problem. Your start batteries are probably 8D's with around 250 AH at 24 volts nominal, if in perfect condition you can pull half that out and they will still start the bus, so figure 125 AH. You need to always figure in the efficiency of the inverter, so add 10% to the output draw to figure input current at 24 volts, so you get your 55 amps at 24 volts. Your start batteries could support that for a tad over 2 hours before you risk not being able to start the bus. They won't be adding anything when the bus is running, so they are out of the equation at that point.
I ran an inverter off my bus charging system to run my 15K rooftop AC quite happily, it was a very good setup for OTR cooling. Sadly my inverter fried itself with a power surge on a switch-over, but that doesn't mean the concept isn't good. Sean did this as well, albeit on a far larger scale. When I replace my inverter I am going to probably size up to around 3500 - 4000 watts, since my AC unit draws closer to 15 amps running at full speed.
Brian