As the other answers said, the general principle here is that the structure can vibrate at several different frequencies, and the shape of the vibration is different at each frequency. The simplest example of this is something like a guitar string, which can vibrate at frequences of 2, 3, 4, etc times the "fundamental" frequency. Google will find plenty of diagrams, and how to show this on a real guitar.
To start the vibration of any particular mode, you have to apply a force (e.g. by jumping up and down) at approximately the right frequency, and you also have to jump up and down at a point that is going to move. You can't excite a vibration mode at the "nodal points" where the motion is always zero.
It's possible that if you jump up and down at a different speed (say 2 or 3 times as fast, if you can do that) you will be able to "move" the bridge at the 1/3 point, by exciting a different vibration mode.
However trying to go from those general principles to the specifics of your bridge is hard, for at least two reasons. One is that because of the suspension system the bridge is quite a complcated structure and it's not obvious what the vibration mode shapes will be. The second reason is that your own mass is probably not negligible compared with the bridge, and the complete system of "you plus the bridge" will have different modes of vibration from the bridge on its own, and also different vibration modes depending on where you are standing along the bridge.
Probably the simplest way to investigate that would be to measure the vibrations of the bridge on its own, and then use a computer "add in" the effect of you standing on it at different points. Vibration engineers do this sort of thing routinely, but it's probably outside the capabilities of a school science lab, and needs a higher level of math to understand what you are doing even if you had the equipment to make the measurements.
