If Aperture is still running on your MBP, you can retrieve the serial number from that version.
Use the main menu command "Aperture > About Aperture" and copy the serial number from the "About" panel.
Install Aperture from Trial version. You can download it as described here: http://support.apple.com/kb/TS4412?viewlocale=en_US
If you originally installed Aperture 3 from a trial version:
- Go to the Applications folder and delete Aperture.
- Download the Aperture 3.1 Trial.
- Open the Aperture Trial disc image.
- Double-click the "Aperture Trial.mpkg" file.
- Follow the onscreen instructions to install Aperture.
- After the installation completes, choose Software Update from the Apple () menu.
- Install the Aperture 3.4 update from the list of available updates.
Your library is not tied to a licence. But you may need to move the library to another disk, if the Drobo is not formatted MacOS X Extended. Aperture requires that the library is on a drive formatted MacOS X extended.
BTW: Your original licence (assuming you bought the licence key from the Apple Store or a boxed retail version) entitles you to two Aperture installations - on desktop, one portable mac. So both your macs will be covered. If you need to use Aperture on more macs you may need to buy Aperture again from the AppStore. The newer licence has better conditions.