And the answer is.....drum roll please....It will not change adCenter at all. The number of ads shown will remain the same. The mainline ad rules remain the same. Ad position will not change (at least not just because of a rebrand - your bidding is what affects your ad position). There will not be any new ad units.
The algorithm changes, but even that's not a change because they're constantly changing the algorithm. Still with me?
What could change is an increase in traffic. With all the buzz surrounding Bing and Microsoft's $80-100 million ad campaign for the new search engine, your ads might get some action.
Let us know if you're seeing any traction on your adCenter ads. Share what you can in the comments.