If you're rich enough to have your own private rail car, Amtrak has the service for you. For $250/year and $2.10/mile you can have your car attached to the end of one of their regularly scheduled trains. (details) This might sound like a lot of money, and for an individual it would be, but what if you split it 100 ways?

Consider the route between Boston and New York. It's about 230 miles so Amtrak mileage charges would run about $500 per trip. With 100 passengers that's just $5/person. Of course you'd need train cars, but a used one at $500K [1] amortized over 10 years and making 300 round trips a year only costs $85 per trip or a bit under $1/person. There are probably many other costs, perhaps even $400/trip worth, but this only gets you up to $10/person. Would people pay that?

Before they were shut down, Fung Wah and Lucky Star charged $15/person running about 15 daily round trips each. Bolt Bus, Megabus and Greyhound probably average about $25 running maybe 10 trips a day. But people prefer rail to buses, so you could probably charge more: Amtrak charges $70-$130. With good yield management you could probably fill 100 seats per trip at an average around $40. That's $30 in profit per passenger per trip.

The real question is, how do you get Amtrak to continue to do business with you after it becomes apparent you're competing with them?

(You might think paying for parking would get expensive, but "no charge will be made at transfer points or terminals when cars are being held for the earliest connecting train or when a car remains with the consist at a turn around location.")

[1] Something like these 1971 Passenger Cars at 115 or 135 seats each. Or look through the rest of their passenger rail cars category.