I think using an Ebay-style auction for the bid would be much fairer (particularly for new players who don’t know what a standard bid is).
Thus you’d place a maximum bid, but your actual bid would be only one more than that of your opponent (or if you tie, then it would choose the bid winner randomly).
For instance, you bid 10, your opponent bids 5. You should win with an effective bid of 6.
This could involve creating one more stage to the game - where you decide how to spend the bid. Or you could submit a series of bids (for how you’d spend 4-10 IPCs for instance). But I don’t think adding a stage on spending the bid would be much of a delay.