Your user license is tied to your user account. So if you log into your account on another machine, you can activate your license on it. What this will do is deactivate your license on the other machine. You can do this either with a paid license or even with your Trial license when you're on the free trial.
So all you need to do is download and run Sitebulb, then sign in as normal.
When you sign in you'll notice that it says 'No Active License' in the top left. Further down the page you should find details of your user licenses. If the license is already active on another machine, you'll see the details of this in red (e.g. in this case I had been using the license on my iMac, and wanted to move over to my Windows machine).
All you need to do is hit Activate License on any of your licenses, and you'll have shifted it across to this machine. If you only have one license, you can activate this on the current machine, and it will deactivate it on the other one. You'll need to go through the same process every time you switch machine.
No, it doesn't - that's the one caveat here. While you can move your license around as much as you like between machines, you cannot crawl concurrently on two different machines using the same license – to do this you would need to purchase an additional user license.