Answer: Both (1) and (2) are correct.
(1) We remain stationary as long as there is no friction but the back of the bus would hit us.
Reason: Our feet are in touch with the floor. If there were no friction, we would remain where we were, HOWEVER, the floor of the bus would simply slip forward under our feet and the back of the bus would hit us.
(2) We are thrown backwards if there is friction
Reason: there is some friction between the feet and the floor. If the start is not too sudden, i.e. if the acceleration is moderate, the frictional force would be enough to accelerate our feet along with the bus. But our body is not strictly a rigid body. It is deformable, i.e. it allows some relative displacement between different parts. What this means is that while our feet go with the bus, the rest of the body remains where it is due to inertia.
Relative to the bus, therefore, we are thrown backward. As soon as that happens, however, the muscular forces on the rest of the body (by the feet) come into play to move the body along with the bus.