From my experience (both as an ex-skateboarder and hands-off bus rider) I'm pretty certain that it would be too unstable to stand on such a board while the bus moves. This is because it's complicated enough to even ride a bus for long without holding on to something if you're standing, so what to say about a board on a spring which is an additional level of instability.
You might manage to stand on such bord while the bus moves if the spring was tight enough, but then there's also a complication of being higher than the bus floor, so if you fall off the board, the impact would be way more damaging both for you and those around you than if you fell while riding the bus without holding on.
So I propose using straps to hold on to while being on the board. They'd hang from the bus ceiling and have handles to grab at different levels for people of different heights. It would still be fun, but way safer. In fact, it would very likely be more fun, because then you'd be able to stand on the board for long and softer springs providing more extreme movement could be used.