As far as I know, there exists no portable version of Calibre for Linux, only for Windows.
The latest versions of Calibre, including portable and Linux, can be found here:
http://calibre-ebook.com/download
Please note that there is some danger in modifying a Calibre Library from
alternating Windows and Linux. The reason is that the operating systems work differently regarding case sensitivity.
So you really should use ONLY Windows OR Linux to run Calibre.
The easiest way to handle this may be to run Portable Calibre from a Windows PC, and start the content server. Then you can access the Calibre library from any PC with a web-browser in the same network. Assuming that the network is configured so this is possible, and you are allowed to use the network like this.
Other methods may involve booting Linux from the USB memory or running Linux using a Portable VirtualBox install, or sharing the desktop using VNC.
But since there seems to be some firm restrictions on what you are allowed to do with the computers and in the network I strongly recommend that you ask first if these things are OK. If you don't it may be grounds for dismissal.