Why does your body go left when a bus turns right?

Momentum.

Momentum is mass x velocity.

Velocity is speed in a direction.

Even if the bus changes direction, you still have momentum in the original direction until some force pushes you in another direction. That takes a moment in a car or bus, so until your momentum is that of the bus, you'll still be going in a slightly different direction, which happens to seem 'outwards'.