When you create a bootable Live USB, what you're creating is more of a LiveCD type if thing rather than an actual install. If you do it with persistence as rokytnji posted, that'll get you persistence but it'll still be basically a LiveCD.
I've taken a Live USB, and after it's booted, ran the "install Ubuntu" icon and installed it onto a second 4G or 8G USB stick. Important to remember to get grub installed onto the USB stick (rather than the MBR), otherwise your machine won't boot without the stick. Anyway, it seemed to run quite a bit faster than the normal LiveUSB.
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