How do I create a 8Gb USB bootable from Windows 8.1 64bit, in persistent mode?
Try Unetbootin or MultiSystem to create the LiveUSB. Both have option to keep changes in Ubuntu-based distros, including elementary. I succesfully installed new apps and packages in Live sessions created by these tools, although not all programs were able to install.
Direct installation on USB drive
Installing the OS directly to USB drive is a bit more tricky. You basically have to select proper USB drive during install of the OS and also put bootloader on the same drive (this option is available when you make your partition scheme manually during install by choosing the "something else" option). You will also have to adjust some Bios settings to boot from this drive (that may apply for the LiveUSB method above, too).
However I failed the one time I tried this (with elementary Freya), although I think it was the machine's fault (cheap Acer netbook, all distros were weird with it).
If you are asking for the steps you can try this link. Works like a charm :)
I've always had good luck with using Rufus USB installer.
It's extremely easy to use, and many examples are available.