The same effect is seen with a vertical piece of metal, such as a bicycle, but is weaker. Because aluminum conducts electricity quite well, aluminum rims help. Steel rims are OK. Non-metal rims cannot be picked up at all. A bicycle with aluminum rims will cause about 1/100 the change in inductance of a car.
It is always possible to set a detector's sensitivity to pick up a bicycle. The trade-off is in longer detection times and the possibility of false detections from vehicles in adjacent lanes. Most people who set signal detectors use the lowest sensitivity setting that will pick up cars reliably.
I advocate using the highest setting that will avoid picking up vehicles in adjacent lanes. Digital circuits used in modern detectors can use high sensitivity settings without unacceptable increases in detection times. Unfortunately, there are still a lot of old detectors out there, and most people who work on signals use principles based on the performance characteristics of old detectors.
In any case, bicyclists should, as a general rule, place their wheels over one of the slots to maximize their chance of being detected. That is where the magnetic field perpendicular to the wheels is strongest. Bouncing the bike or moving it back and forth does no good. If you have a metal frame, another tactic that may work is to lay the bicycle down horizontally inside the loop until the light turns green.
Advancements are under way that may make traffic loops obsolete some day. In particular, radar, infrared and sound detectors have been introduced. Systems based on video cameras are especially promising. Such systems can easily detect bicycles. Such a system may even be able to detect pedestrians some day.