Most likely his money is managed in a blind trust, which means he has no control or knowledge over how it is invested. For all he knows, inflation will help his portfolio. In the most likely event, his money is invested in a mix of equities, stable funds and bonds, and all his money does is track the general health of the economy (with a smaller upside/downside due to hedging and diversification).
What I would argue is that Bankers and Wallstreet just want it to go back to what it was. They're trying as hard as they can trying to build a time machine to go back before everything fell apart, and resisting all attempts at changing for the better. They just want this to all go away. So given the choice they want that lever to make everything as it was before which is impossible.
You're also dismissing the social wins aspect of this: you definitely can't argue that Bernanke doesn't know the way his friends are betting, even if he's "blind" to his own portfolio. Bernanke doesn't have to win directly off this for there still to be a possibility of him making corrupt decisions that help both him and his social network.
Bernake doesn't know what's in his portfolio, because his money managers don't tell him. That's why many agency heads are required to put their money into a blind trust. If you have evidence to the contrary, by all means notify the proper agency (I think OTS, not really sure).
As for Bernake's friends, I expect most of them don't tell him (or anyone else) how they are betting. If I tell you my trading strategy, you can turn around and take my money.