Learn English – what is the meaning of “I work long hours”

The lyrics are as follows:

Come on, come on, turn the radio on
It's Friday night and I won't be long
Gotta do my hair, I put my make up on
It's Friday night and I won't be long

Til I hit the dance floor
Hit the dance floor
I got all I need
No I ain't got cash
I ain't got cash
But I got you baby

In this context "I won't be long" means that Sia won't take take too much time to do her makeup and get ready. She wants to dance with her partner sooner rather than later.

If you click the button on a similar form I found, it brings up a choice of a number of hours, so my guess is that instead of charging you to go from one place to another place, you can reserve the car for a number of hours and it will take you multiple places. To "go by the hours" is not idiomatic.

What they probably meant was "I want to rent/reserve by the hour". For example,

With Legends Limousine, you can reserve comfort and style by the hour. (Source)

This means that you pay an hourly rate, or a fixed amount for each hour that you have the car service.