I have used such lift-gates at work, and they are definitely a great invention. Installing it on a bus would be a major project, but everything is possible with enough time and money.
You will have to lengthen the lift deck so you can get all four tires on it, and this may not be easy -- but everything is possible with enough time and money.
But I'm thinking you may be able to build a ramp that you drive up on. First, you would "beaver-tail" the floor in the bus, with a gentle enough "hump" that the car can drive over it. Then you would build a bi-fold ramp, like in the drawing below. Drive the car on, lift the ramp to level with an electric winch or two, and drive in.
Here is what I have:
Come to think of it, if you beaver-tail the floor a lot more than I did, and use a full bi-fold ramp, you may be able to just drive the car right in. I beaver-tailed mine just a little bit, to have room for a trailer hitch.