What will increase output volume (dB) on a Piezo Transducer?
10 Vpp is NOT the same thing as 10 Vrms. In order to get the full output from the transducer at 10 Vrms, you're going to have to drive it with a 20 Vpp square wave, or a 28.3 Vpp sine wave.

With a single supply and an H-bridge driver, you will need a 12 to 15 V power supply in order to get there.



An alternative would be to build a relatively high-currrent bridge driver that runs directly from your 3.7 V battery, and use a 1:5 transformer to boost the voltage to the level the transducer needs.