I think I could make out on the tag the letters VT. If so, when that bus left the factory it had the Cummins VT555. Which is better known as the Triple Nickel.
There is no way in the world that bus has gone 300K+ miles on a 555. 100K would have been surprising.
If it has been repowered it may have had a Detroit 8.2L, a Cat 1160/3208, an IHC DT466, Cummins 5.9L, or a Cummins 8.3L. Or if they were really adventuresome they might have put in a Cummins L10.
The most common repower choice was the Cat engine because if was an almost bolt in replacement since the Cat was an option from the factory as well.
I would be interested in knowing how the bus has been used over the years. If the bus was purchased brand new by the Y it must have had someone who was birddogging the preventative maintenance or the bus wouldn't have made it this long. If the bus was purchased used from someone else it would be nice to know who it was and for what it was being used. A mine shuttle bus from WY would have close to 200K miles put on in five years. 100K miles by the Y over the rest of the years sounds credible for the rest.
As to how much life is left in the engine about the only way to know for sure is to start it, get it warmed up, take it for a run and run it up and down through the gears to make sure everything is working correctly. And then take an engine oil sample and have it analyzed. That is about the only way in which to make a somewhat educated guess.
Personally, if the bus started from stone cold and ran smoothly and didn't smoke very much I would take the risk at $2K. At $1.5K I would be all over it!
This is a case of if the bus body is good enough the bus is worth it just for the body. A newer bus with a better power package can be purchased later if need be. In the meantime you have a nice bus that is equipped for trips. Translated that means it will have highway gearing and enough HP and torque that it won't slow down to walking speed on every hill.