What is the cheapest option to fetch a person over a long-distance with bicycles?
When I drop my wife off at the train station, we use a folding bike and a trailer. She rides the folding bike there, and her suitcase rides in the trailer behind my bike. However, while inexpensive used folding bikes can be found, getting a trailer may be too expensive. 

You'll either need to carry someone on your bike, or find a way to bring along another bike. 

You can hold onto another bike while you're riding, wheeling it along next to you, but that's not very safe (especially for rides of any distance). Since you've indicated you don't want to carry someone on your rack, I would consider buying an inexpensive beater bike and a truck bed mount, attaching the mount to a bike's rack to receive the front fork of the bike you're pulling. (Here are instructions to make one of those inexpensively, scroll down a bit on the page and you'll see a commercially produced version of the same device.) 



You take the front wheel off the towed bike and the bolt shown goes where the axle of the front wheel used to. Works like this:



You can ride with one bike behind the other, strapping the front wheel of the bike you're towing to the side of your rack, or just carry it. You'll also have the empty rack for the trip back.