Here's how we do bid distribution on my campus: Instead of individually calling them into the office, our Gamma Chis (Rho gammas) are given all the bids for the girls in their original groups. Bids are handed out to the girls and then all the groups open them simultaneously. Then the girls gather into groups with girls who got bids from the same chapter they did, and then as a group they go to the sorority house.
We were called the night before bid day by our Rho Chi and told either that we got a bid or that we didn't. If we did get a bid, we went to the Student Union during a certain time the next day (Bid Day) and picked up our bids. The bids told us to be somewhere on campus at 5pm that day to meet our pledge class. Then the seniors and pledge educator picked us up and we drove around campus and over to the house.