I vote for the push-pull circuit that Zero999 showed first, but with some modifications.
- Add diodes across the base-emitter junctions, but pointing in the reverse direction. This will protect the transistor and speed up the switching.
- Add diodes across the collector-emitter on both transistors to provide free wheeling. Similar to the body diode in a FET.
- Adjust the coupling capacitance to match the switching frequency and the transistors. 1uF will probably not work for 1 MHz, but a ceramic 1nF will be closer to what you need. Double check that the capacitance is enough to keep the transistors on for the needed period time.
Also the 1k in series with the input signal might be too much, try 47-100 ohms.
- Consider to add a small resistor, 5-10 ohms, and a matching inductor in series between the driver midpoint and the piezo. With 2 nF you can start with something in the range 10-33uH and observe the waveform at the excitation frequency. The driver will give a square wave output and you want a sine wave over the piezo. I have seen more than 45 V over a 1 nF piezo at 1 MHz with only 15V supply for the driver.