Let me share one small experience first. I have window 7 64-bit with 64-bit IE installed on it.
Just since there is Facebook chat feature on bing bar I added tool-bar and it was really nice. I was over joyed!! that I can chat without log-in into Facebook website. I chatted, closed the IE, after sometime reopened and to my surprise there was no BING tool-bar. I checked everything, everything was fine but there was no bing bar :( !!
Then after few trail I realised that I have 64-bit version of IE running. So just to check I browse to path "C:\Program Files (x86)\Internet Explorer" which is 32-bit version of IE.
I clicked on "iexplore.exe" and hurry !!! the IE opened with BING bar.
Later I created short-cut for 32-bit IE. Till now I have not found any performance different 64-bit & 32-bit.
Happy BINGing !!!!