People who are new are the ones most likely to use the NPC shuttle.
My first time I was so confused at the 7 ETA times... I thought I was stuck too, thought it was a bug... I would think YAY i have arrived to watch another hour be added on.
I wish for the sake of new players sanity they fix this to actual ETA. Little things like this can make a new players not return.
If you are the pilot it will be on the sidebar, and viewable at the top of the Cockpit page. If you are not the pilot, you will have to ask the pilot. If you are on the NPC transport, there is no way currently to find out.
You wil just have to wait until the journey is finished, if you tell us where you started from, where you were headed and when you started the journey some brainy person will be able to calculate how long you have to wait