First, I'm assuming you're actually using Mozilla Firefox, rather than just setting the homepage of some other browser to Firefox's own homepage. Your question is misleading because it says "running Firefox as my home page". Firefox is not a home page; it is a web browser. Firefox, being a web browser, can have a home page within it, which means that it's the page which loads when you first start the browser, or click the Home button on the screen.
You didn't state which version of Firefox you are using, so I'm going to give you instructions (and a screenshot) for version 14.0. If you can't figure out these instructions for your version of Firefox, post back.
Step 1: Go to Tools -> Options in the menu bar. Alternatively, if you don't have a menu bar but you do have the big orange "Firefox" button at the top-left of the screen, click it; a menu pops up... navigate to Options, then another menu pops up, then click Options.
Step 2: Immediately in the "General" tab, your homepage should be displayed.
Click "Restore to Default" to set the homepage to the Firefox default, which is http://www.google.com/firefox.
If you want to set your homepage to hotmail, just enter http://www.hotmail.com into the "Home Page:" box and click OK. You can set the homepage to anything you want; you can even set it to a bookmark you have. Feel free to explore the options in there; it's hard to break anything.
By the way; the reason your homepage was sent to Bing is probably that you installed the Bing Desktop client from Microsoft, either through a suggested Windows Update, or by going to Microsoft and downloading it.
Did you installed any new software early on your system, this could be the reason of that and most probably if you have installed a Microsoft software then it is surely done by that. – avirk – 2012-08-21T13:19:44.323