You could apply the wiggle expression to one axis (google wiggle Y axis expression). For the amp variable, you need to select it and pickwhip it to the slider value of an expression control effect which can be applied to the text layer or to a null layer. Then, finally, you animate the slider value from a high value to zero to make the text settle.
The animated slider effect controls the wiggle expression which controls the Y-position of the text.
If you want to see the wiggling text more than once over the running time of the comp, you may want to avoid applying the slider to a null -- just apply the slider to the same layer as the text, get it right, then dupe the text layer and retype the text if necessary.