The stunt bike I believe has small gas motors inside the wheel hubs not sure if both or just one, but the designers and Nolan said the in universe bike was meant to have an electric motor in each wheel hub which is why it has the sound effect that it does. Side note: It's called the Shepard tone and it's a pretty interesting audio phenomenon that when you layer ascending sine curve tones it creates the effect of a constantly ascending note:
With electric motors in each hub the vehicle could use those motors for both acceleration and braking, eliminating the need for anything other than electrical lines to front and back. Electrical connections are easy to transfer through rotating parts as proven by cheap light up fans. The things it does are all theoretically possible with extensive lines of code and electric motors front and back.
Whether the stunt vehicle has every detail featured to make that believable is another question but honestly we don't see it in enough detail on screen for that to matter.
As for the sideways rotating over the wheels, this is theoretically possible but I doubt Batman finds it a smooth ride. It looks pretty smooth to us but so does a formula 1 car and I can guarantee those dont provide a supple ride. As long as Batman can hold on and the unevenness of the guns is not so much that it shoots the bike into the air it wouldn't really matter how smooth it is. It's way more plausible than literally any CGI vehicle in an MCU movie.
edit: Think of the Bat-pod rotating sideways as a Segway with lumpy Wheels. If you have gyros in the body to make sure it stays upright, just like a segway, and it’s built robustly enough then it’s very plausible. The way it behaves on screen shows it keeping Batman angled a bit away from the direction of the roll which would help him not get thrown off. His momentum is driving him towards the seat so gravity and momentum are insulating him from getting thrown off by the bumpiness.
No, I'm not.
