Jumping out of a bus: A physics challenge!

If you have studied Physics at least upto Higher Secondary level, you will be well aware of inertia and its plays. And here goes a popular question; why do we run forward after jumping off a running bus? You should notice that 'forward' is highlighted. When I asked this question to a post graduate in physics, he felt it insulting!
'Who doesn't know that it is inertia? Don't you treat me like a school boy!'; that was his reply.
Well, after asking this to a lot of people I feel this is not a school-time question. If you also say 'It is obviously inertia', you should answer this question;"Then why do you jump forward?" Let me explain this question a bit: Here, what you mean by inertia is your inability to come to rest by yourself, since, before jumping out you were moving forward with the velocity of the bus. If you don't nullify the effect of that velocity you will fall forward, right? I hope you don't disagree upto this point. But the crucial question here is, if you jump forward, how will you nullify that effect? You are just adding extra velocity to that forward velocity! In order to cancel the effect of a forward velocity, you have to introduce a backward velocity, not a forward one. So it means if you jump off a bus and run forward, you cannot cancel the effect of inertia.
Most of you may not agree to this because your experiences tell the reverse. But I didn't say you have to jump backward next time while jumping off a running bus. I just said, you cannot cancel inertia by jumping forward. Actually, the answer to that question is not purely physics but at the most physiology! If you are to cancel the inertia effect, physics tell you to jump backward. But the physiology of your body is not suitable for that. As long as you cannot jump back with a velocity greater than that of the bus' forward velocity, your resultant velocity will be along the bus' direction and you tend to fall back. Now because human body cannot prevent a backward fall, you should not do that. Human body is well equipped to prevent a forward fall (that is what we do while walking and running) with two legs and that is why we jump forward although it increases the effect of inertia.
Still don't agree? Suppose you throw a glass bottle from a running bus to the road. When will it break more easily, when you throw forward or when you throw backward? The answer to this question will solve our first question well.