Is there a such thing as a driving service that isn't a taxi

Is there a such thing as a driving service that isn't a taxi that will drive you far and back?
& will also wait for the trip back some number of hours afterward 15 hrs?

Sure, rent a limousine. that's what they do.

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It is not just the stretched Cadillac with a bar in the back. Many Limo businesses have regular vehicles available a reasonable prices, on occasion less than a Taxi. Taxi's are great on short notice, but if you may be able to plan ahead a Limo is the way to go.

greyhound or a train

a bus? a train? a rental?

I do not know if there's but it sounds like a service I could certainly use. it is a great Idea pursue it. I like to go to concerts but generally have trouble finding a chosen driver, and I live 40 miles from the concert venue. I could certainly pay to have transportation to and from a situation like this. here is a star, best idea I have heard all night..

nope.

greyhound bus is your answer

it depends on the city, in some cities they may have
a car service, or you could verify with a Limo service
as well they have small sedans also
but I am figuring a limo service could be your best bet

They're called limousines. They have executive cars, typically Lincolns, that have a driver. I am sure they are not real cheap.

yeah a bus.

You can hire a limo sevice to come to your home to pick you up & take you some place, like say a night club, then take you home again when you're too drunk tor drive yourself. This kind of service tends to be costly than taxi service.

Some taxi drivers are independent freelancers and you may be able to make alike arrangements with them.

There are services that carry disabled and elderly.
Through those services you may be able to contract in advance for a driver.

Same kind of deal with the bus businesses.
They make most of their money driving different routes, but they may also be contracted with to do a special run.

Do you ever see a "tour bus"?
All types of special clubs can arrange a tour just for their interests, in which they contract with a bus company to offer the bus, driver, different equipment so that someone may be in front telling the passengers what important & useful landmarks coming up.

Same kind of deal with a train.
Your group can arrange to have some extra passenger cars added, that are just for your guys . at the destination, those cars go on a separate line . while you visiting whatever city, you use those passenger cars as a motel, then when everyone done, the train haults the special cars back to the start city.

You can charter a private plane.
At destination, the plane and pilot wait for your return, but it's polite to give them an idea how long, so the pilot can get some sleep, meal, use the bathroom etc.