I use a variety of methods. If I'm going from A to B where both are a long way from home, I'll use a one-way car rental. These are pretty reasonable compared to a plane ticket and shipping charges if you can make your destination in 24 hours. They are more reasonable for multiple person tours. I then rent a return car at the end of the tour.

If I'm riding a loop, I'll drive my own vehicle. Not all that cheap but much less of a hassle than an airplane. Recently, I drove my vehicle to Nashville, toured the Trace to Jackson, put one of our group on a plane there and drove a one-way back to Nashville. I parked at the long term parking at the airport. It was certainly easier to carry 3 bikes, 2 tents, 3 sleeping bags and 10 panniers in my truck then try to get them on a plane.

Although trains sound intriguing (and I've used Amtrak from St. Louis to Warrensburg for the Katy), they are slower and much more of a hassle. They don't connect with other lines all the time which means a bus ride and passenger trains have the lowest priority on the lines. If freight needs to move, you could be stuck for a while on a siding. It also takes longer than driving your own car for any appreciable distance from home.

Just be flexible.