What operating systems are being used for which computers?
Along with the answers to the questions above, be sure to give the full specs. of the external HDD and its connection.
Yes, I have some ideas if the following two assumptions are both correct:
1) USB 2.0 drive - confirm this is the case, or tell us what it is (firewire, USB 3.0, etc.)
2) Windows OS - which version on school PC and your mates; or is it Apple, which one, etc.?
Check to insure your are not going through a USB 1.1 hub (for example if an external USB 2.0 drive is plugged into a monitor hub which is plugged into the PC, then your speed may only be USB 1.1 - too slow for Premiere)
And, make sure Windows policy is set to "better performance" instead of "quick removal" (the default) for your USB drive.