Without having tested this myself, I have to say, I don't think you could run Visual Studio from a USB (i.e. install Visual Studio to the USB without installing any files on the PC).
But most likely, you could have your build tools on the USB and use a different editor that could run straight from the USB. I don't know of any that would be good enough to provide a replacement for Visual Studio but depending on what you're going for it might be an option.
A different approach would be to put a virtual machine on the USB drive and have Visual Studio installed in that virtual machine. Then simply plug the USB in, and launch the VM. Still, I'm not sure if you could have VMWare Player run off of a USB drive.. Maybe VirtualBox. In fact, there's this post to support that theory: How To Install VirtualBox in Your USB Drive. Once you get VirtualBox going from the USB drive, setting up a Windows virtual machine and installing Visual Studio and whatever other tools you use should be trivial. You could also enable File Sharing between the host and the VM and store your project files on the USB drive if you need to have access to them from outside the VM as well..
Good luck! and let us know if you find a different option..