Strange. They should be accessible without rebooting. Even when it detects it for the first time and dusts off the mass storage drivers buried within windows, it should just say "your hardware is now successfully installed and ready to use" or something like that, then you use it.
Actually, it sounds like you've got a drive letter mix-up. You say you're at work, so I assume you've got a network drive allocated to something like D or E or F, after your physical/logical hard drives. The USB drive wants to assign itself the next letter after that, which the network drive may be using already. Booting it up with the USB drive already it causes the PC to detect it as a peripheral before assigning a drive letter to the network storage after it connects to the network.
SO: I reckon you just need to stick in your USB drive and reassign the drive letter to one that the network drive isn't hogging.
Right-click on My Computer and click on Manage. Click on Disk Management in the bottom left, and now on the right hand side of the window you should see a list of drives. At the bottom of this section, click on the part that says something like "Removable Disk 0", and right-click on the main bar part of it and select "Change drive letter and paths". Select a new letter for the USB drive, something like X or Z that a network drive won't use, click OK when it says "doing this will cause the world to end and all data everywhere be erased forever" and voila, you should now have the drive appearing as Removable Disk (X: ) under My Computer.
Reassigning the drive letter to this device will cause it to remember to become X (or Z or whatever) every time you put it in this PC. If you use it on someone else's PC in work you'll need to change the drive letter again.
Hope this helps, I'm pretty sure that's what it is and my description may not be 100% - I'm in university at the moment and access to the Computer Management window is disallowed so I'm doing this from memory (tech support placement last year

).