Do I have a case if I hit a bus from the back and airbag did not deploy?

Yes you would have been experiencing the injury with or without airbags. They only lessen the impact of forces in play. If you PIP or med pay coverage get the info and open a claim with your own company to pay the bills. Unfortunately you have not claim for injury you can pursue. You were the fault party for your own injury. you were over driving existing conditions. So get better and drive safer.

If the sensors that control the air bags were contacted, and the bags did not deploy, you may have a case.

If you have to ask the question as to whether your pain is related to the accident, you can be sure that the car manufacturer, a judge and/or a jury would be asking the same questions as well. To answer the question, you would need an automotive engineer expert or two to give an opinion(s), and that is expensive. Unless you have a severe condition that is definitely related to the airbag's failure to deploy, the cost of getting your question answered will probably outweigh any potential recovery.

Airbags are not designed to be magic. They are designed to stop serious injury. in your case that was not necessary. And 2 months later you seem to notice a problem? The insurance co will laugh at you? airbags? How old is the car? is it under warranty? Ever been damaged before? Can you prove causation as to airbags? Can you prove causation as to back? You don't have much of a case in any event.

You would need to have your vehicles Event Data Recorder (EDR) data downloaded and analyzed by an expert to determine if your air bags should have deployed (they likely should have if you struck a bus @ 40mph with the front of your vehicle). They likely would also have to look @ the vehicle in it's damaged state, look @ the air bags, the air bag sensors, the vehicle crush, etc. to determine why the air bags didn't deploy. If the bags should have deployed, you may have a case against the vehicle manufacturer and/or the air bag manufacturer and/or the sensor manufacturer. However, you should note that these cases can be quite expensive to prove/pursue and your damages will have to be sufficient enough to warrant the expenditure of the costs. As you correctly point out, you'll also need an expert on the biomechanics/injury mechanism to determine whether you would have suffered less serious injuries had the air bags deployed. It's probably best to consult with a local Michigan product liability lawyer for input and advice.