Each time you pick up ammunition, every member of your party receives ammunition as though they had picked it up. This is different to the way gold and eridium is shared and there is no indicator to show that you have gained ammunition as a result of one of your party members picking some up.
The below is quoted from one of the discussions as a result of testing the behaviour of this mechanic:
When you or your friend collect ammo it goes to all players. It isn't like 5 bullets go to each player or some crap like that. Everyone gets every ammo drop ever. Yes it works. It is the same for cash and eridium...the only indication of you getting ammo is if you are in your backpack at the time watching it.