Hriston
Dungeon Master of Middle-earth (He/him)
I believe that surprise happens outside of initiative, or after, but disregarding initiative.
Initiative actually plays an important role in how surprise works. It tells you how long you are surprised. You are surprised from the beginning of combat until the end of your first turn in initiative order.
The PHB says that you compare the stealth roll of the ambusher with the Passive perception of the ambushed.
In this case, you roll for the bulletes, and compare that to the Passive perception of the players. Those who have a PP under the rolled number are surprised, and cannot take their first turn of combat. Basically just "Lose a turn" in the initiative order, and wait until it rolls around again. Any players who have a PP over the rolled number fight in whatever order they got for initiative.
A minor correction: A hidden creature also remains unnoticed in the event of a tie.
On the other hand, if the entire party has the Alert feat, this is all meaningless. It states you cannot be surprised while conscious, so you simply don't get Surprised.
A Stealth/Perception contest is still useful for determining if the party detects the bullettes before they come out into the open.