Well in a normal (at the board) game, you will find that the person who starts the bidding has the advantage, because the following players need to beat, rather than equal the first player's bid.
So, one option you have (and the one I would use) is a blind auction, where if there is a tie, then the order of bidding is the person who wins. Obviously, the way you do a blind auction is difficult over email as you cannot prevent the other person or persons from seeing your bid, unless you do one of two things
- Have a 'referee' for want of a better word, who collects the bids until all are received and email the results once collected.
- Have a player (possibly the final player in the bid order) act as the referee, who cannot bid themselves, but collects all blind bids.
However, I would suggest looking for one of the online board game sites that allow you to play turn-by-turn. There are a few that do this (I believe there are already questions on this topic), but I am not sure if there is one for this game.