Well Google does not have such power to do that on it's own right, I suggest getting Malwarebytes (if you don't have it) and installing it, then fully update it (which it will ask to do as it's 1st job if freshly installed), then run a full scan just for peace of mind, if anything comes up then you will be best served in the Virus section, where the Pro's can instruct you on using various software to check and remove anything that should not be there.
But let's check the basic's before going down that road, you don't mention which OS you have so I assume that the problem system is running that which you list in your profile (but it doesn't mention if 32bit or 64bit) ?
So lets try the manual setting just to check, launch ie then go to the Bing homepage that you want to use, then click the cog icon near top right of the browser, 2nd from bottom is Internet Options, click on that to open a new window.
Now the new window should be showing the home page, set as google from what you have said, it is probably highlighted already going by mine, if so hit the Del (Delete) key to remove it, now click on the button that say's Use Current, now this is the important bit, you need to click the Apply button near the bottom right of the window, then click OK to close the window, now close the browser and open it again, what does it came back as ?
There are a few ways to do this, but if you have been trying those already without success, I figured it can't hurt to try a slightly different approach, try this and let us know how you get on, then we can go from there.