Using Piezo Vibration Sensor with Pull-Down Resistor - Arduino
Looking at the AD inputs on arduino, they are not a good match fordirectly reading those piezo sensors. First, the AD inputs need a relatively low impedance source:

[Edit: I had posted the wrong link]
Arduino Analog Input example clarification
[End edit]

So using a 1meg resistor with the piezo is essentially a 1meg source impedance, which is far away from a good situation, and as you've observed, results in drift.

Further, piezos have very poor low frequency response, so slow bending will produce low output, especially with smaller values of resistor.

For better ways to condition the piezo signal, follow the sparkfun page links to the Technical Manual, page 36 Circuit Basics.