So my understanding is there are 2 things at work here with your snappy bumper.

The strength of the magnetic field is determined by the number of windings times the current divided by the length of the coil (not the length of the wire). The more windings, the stronger the magnetic field.

The other key factor is the response time. Remember that inductors are an active power element that resists sudden changes in current. At t=0 the current in coil for the pop bumper is zero. Once it is closed in, it takes time for the current to build in the coil as the coil resists the change in current (Impedence). Impedence is directly correlated to the number of turns in an inductor coil. So the more turns in the winding, the slower the response to a step function change in current.

*Brain fart* inductors are passive elements, not active like I said above