You're misunderstanding something.
When you call the Blimp contact, the woman says:
We'll sendOf course, sir. I'll get one sent out to your nearest locationthe nearest available drop-off point.
Or something similar. The thing is, unlike a cab, that can go almost anywhere, a zeppelin is huge and can't simply land whereever.
Calling the Blimp makes its icon appear on your map. You have to go there yourself.
###EDIT:
This is the exact quote of what the woman says:
Of course, sir. I'll get one sent out to the nearest available drop-off point.