I think I have figured this out. It is working consistantly for me.
1) open new browser and go to msn.com or bing.com
2) make sure your are logged OUT of your live or hotmail account by examining your status on either of these pages. Logging out clears a credential cookie or something??
3) go to hotmail.com/m the mobile version of hotmail. login there.
4) close the mobile hotmail window and go to bing.com
5) on the bing page ...find the hotmail link and click it.
6) a micro$oft nag screen will complain you don't have a compliant browser.
7) On this page, select the ignore go on to hotmail link.
hope it works for you. The credential will be cached for hours/days?? but will finally expire. Hotmail will complain that you must relog in. GOTO 1)