The airbag will not deploy in a small bump. It needs a big bump to operate, as in Europw they are an additional restraint to the seat belts.
In some American states seatbelt wearing is not compulsory. They have two-stage airbags as a result, often triggered by sensors in the front bumper. There have been a few instances of airbags going off in car parks, but even then it is a significant bump.
In Europe, where seatbelt wearing is mostly compulsory, the seatbelt is the primary restraint, absorbing most of the impact forces as it stretches. If the impact is severe enough, the airbag will be waiting for you as you get there. They are self-contained, so the trigger sensor is in the airbag device. It is an inertia device, requiring considerable force to trigger.
So don't worry about it. As said above, if the airbag has gone off, the front of the car will be well squashed.