Clone one partition and boot from USB

I have small problem: my hard drive has 500GB storage and it is divided into partitions

/dev/sda1 - 20 GB (boot)
/dev/sda2 - rest

I want to clone only one partition

/dev/sda1

and write all data on my USB stick

/dev/sdb

What's more I want to make my USB bootable and I don't know at all how can I do that (if it is possible to clone only one partition and properly modify MBR in order to boot from USB).

First, does your PC support USB boot?

Yes, without any problems.

Maybe see if you can get a bootable Ubuntu image for USB and install that, then put your Ubuntu over it, or in a subdirectory where you can cross-mount it. I am not a usb linux boot guru, but maybe there is one around. ubuntu\ usb\ image - Google Search