I don't see any benefit in bidding late.

If there are two bids in a round then it will go to the next round, so if you bid with 20 seconds, or with 1 second left, you only win if you are the last bidder.

Getting the last bid in on a round is only important if its your last Token and you are hoping the person you are bidding against will have run out. If you are going to bid more than the current round then get the bid in early so you know its secure.

All a late bid does is get you in the driving seat if there is no bid in the next round. If your opponent is another late bidder then the chances are you will late bid in the next round even if he doesn't to make sure you get your player. The downside is a server lag, or simply a loss of attention when timing bids will mean you lose.

I always bid early in the rounds. I bet I've got several players due to others trying to late bid and missing.