Currently dual booting Ubuntu and Windows relies on using the BIOS's 32-bit bootloader. However booting sometimes results in a blank coloured (typicaly purple) screen so switching the OS requires a cold boot through the BIOS using the F10 option.
This 'F10' dependency can be removed by simply re-installing Windows as a 64-bit version and the switch is free (i.e. you don't have to pay for it) as long as you have a qualifying Windows license (see How to migrate to Windows 10 64-bit from 32-bit versions of Windows).
The whole process to configure dual booting is essentially straightforward and consists of three parts. First you need to prepare a USB for the Windows 10 64-bit installation. Then you need to install Windows 10 64-bit from the USB. Finally you need to download and install Ubuntu and configure dual boot.
Because the switch from 32-bit to 64-bit Windows requires a new installation (meanings files, applications and settings will be deleted) you will also have to install native 64-bit drivers. I've created a video of instructions with screenshots (see https://youtu.be/UQPCYwz-PK0) which covers the process in more detail and will assist anyone wanting to dual boot.
Before you start you will need:
1 x CS125 (STK1AW32SC) with Windows 10 installed
1 x USB
4 x hours
1 x backup (optional)
and the following links:
Windows ISO: https://www.microsoft.com/en-us/software-download/techbench
Intel Drivers: https://downloadcenter.intel.com
Ubuntu ISO: http://linuxiumcomau.blogspot.com/2016/06/running-ubuntu-on-intel-compute-stick.html
Remember to take a backup of any files you want to keep before you try this as otherwise they will be erased during the installation. And don't try going from Windows 8.1 to Windows 10 using this method as you'll probably end up having to pay for a Windows 10 license now that free upgrades have finished. Also this will not work on the first generation BayTrail Intel Compute Sticks (STCK1A32WFC) as the BIOS is not compatible with the Windows 64-bit ISO.