Hm, not sure if that's the way it works Vlossk.Edited By: Nicholas Haines on Year 9 Day 262 5:33
As far as I know, you must move inside of an NPC Starport. When inside, click 'Actions> NPC Transport/Offplanet Transport?". You then should get a list of destinations, with the prices listed for each destination.
Click the check box next to the destination you need to go to, and click the 'Go' button, or whatever it's called/ whatever resembles it.
After that, the funds will be deducted from your account and you will automatically be transported to the shuttle, and it will begin the trip.