To break this down somewhat, you're proposing in effect two separate (or at least, separable) changes here. Firstly, making bidding more interactive (both/all parties bid on each 'action'); and secondly, putting it _after_ the die roll. One could equally try one of these without the other; or other combinations, such as having a 'round' of betting before the die-roll, and another one afterwards.
Another consideration is, how precisely to tie together the betting, and the associated description. Presumably each fresh bet requires 'upping' the corresponding game-world (intended) consequences somewhat.
> Obviously someone with lots of AP has an advantage in being able to
> bid other people out of the contest but that's also true of poker and
> it isn't always teh person with the most money that wins.
There's obviously the issue here of what you consider to be "all in". To replicate the general effect of HQ bidding, you'd have to allow anyone to 'call' any bet, no matter how negative it put them, but only those eligible to make desparation bets would be allowed to 'raise' themselves more than they 'have on the table'.
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