If the first Province gained is is on the same turn that triggers the end condition (e.g. 3 pile), does the Mountain Pass bidding still happen or not? (the base rules say to end the game, but the Mountain Pass says to do the bidding after that turn - which rule overrules?)
Look at the rules carefully. The original Dominion rulebook says "The game ends at the end of any player's turn when...".
And "Mountain Pass" happens "after that turn".
After that turn is later than at the end of it. The game ends before Mountain Pass has time to trigger.
(And, when you think about it, this is likely why Mountain Pass was worded in such a way. Otherwise, the person to the left of the current player just bids <40> and gets 8VP for free.)
By analogy, Caravan says to draw a card at the start of your next turn, but if the game ends before your next turn, you don't get to draw a card. Likewise, if you buy Mission and the last Province, you don't get a Mission turn. Or if your opponent plays an attack and you set aside Horse Traders, but your opponent then buys the last Province, you don't get to return Horse Traders to your hand or draw a card from it.
In short, it's entirely possible to trigger an effect, but then end the game before that effect can be carried out. Mountain Pass is no exception.