How to install iTunes 12 64-bit version?

You can't arbitrarily select which version to install - you must use the installer that's compatible with the release/edition of Windows that you are using. You may be seeing the consequences of the fact that the 64-bit version of iTunes is not *completely* 64 bit - the main application is still 32 bit and will therefore, on a 64 bit system, be installed in the Program Files (x86) folder. Other components are, however, required for correct operation with a 64-bit version of Windows. If you download iTunes from the primary source (http://www.apple.com/itunes/download/) scripts on Apple's webpage will detect the architecture of your PC and only offer the correct version for it ... though there is some anecdotal evidence that those scripts may fail for some users, and you may need to go directly to the relevant downloads:

• iTunes 12.0.1.26 for Windows (32-bit) -iTunesSetup.exe
• iTunes 12.0.1.26 for Windows (64-bit) -iTunes64Setup.exe

See turingtest2's notes on Troubleshooting issues with iTunes for Windows updates for more details if you're still having problems with installation.

I made sure to install the 64bit version of iTunes 12 to my new Win8.1 machine, and it too is only running at 32bit when you look at it in the Task Manager. I also verified the installation files are in my C:\Program Files (x86)\iTunes folder and still it only shows as running at 32bit in Task Manager.

That is correct. iTunes itself is a 32-bit application whether running under Win32 or Win64. The "64 bit" installer includes other components and services that are necessary for iTunes to operate correctly in a 64-bit Windows environment.