Alternator has nothing to do with bus starting on a brand new battery. You have a disconnect somewhere between the starter and the battery. That was my point.
If you have wires showing through the insulation on the cable, replace the cables. They can arc to ground and short out if you have a tight battery compartment. Shorting out could possibly lead to a fire. Noone wants to see you driving a 30+ foot flaming 27,000 lb torpedoe.....well maybe Cal does....
Fix one problem at a time. You will get 600 different check this comments about 4 issues in 1 day.
Brake lines are hydraulic, air hoses are air brakes. Does your bus run for 15 minutes and give off that hissing noise a semi does when it parks???