[ubuntu] Boot question

Here's the background: At work I have Ubuntu installed on an exteal HDD (been doing this for quite a while) and boot from it. I work in various computer labs so I can take everything with me and for the software that will only run on windows I have virtualbox with a virtual PC that I put a standard work software image on.

My problem is that for this month I'm in a new lab where the staff PC is one of the new lease which is an HP 800 G2 (all in one) and the BIOS refuses to see my USB HDD and thus I caot boot from it.

Can I boot from a USB flash disk and use the system installed on my USB HDD? I will be rotated out of this lab at the end of the month but as these PCs are the new lease they will spread to all other labs and the lease cycle is 3 years.

* to add/edit, the HDD is perfectly viewable once the system is loaded in-case that wasn't clear. I'm writing this from portable Firefox on the NTFS partition of that drive.