First, measure the capacitance- that is the most important parameter for driving them. Probably a few tens of nF. The other parameter is resonant frequency, but that is influenced by the design of the cavity you mount them in. The acoustic output will also be heavily influenced by the cavity design and the mounting method.
The vibration mode of this kind of element is oil-canning so there is a mechanical null line that forms a circle concentric with the element. Usually we try to use a molded plastic knife edge at the null point for mounting so as not to damp the element/cavity resonance too much.
It is preferable not to put DC across the elements, so you can drive them (to some level of volume) with a GPIO pin and a series capacitor. The only danger of that is that shocking the element (tapping it, for example) will generate voltage (like a piezo BBQ lighter) that could conceivably damage the MCU. You can slap some Schottky diodes in there (BAT54 for example).
Another method that will give you more volume is to drive push-pull using two outputs (in which case you may not need the series capacitor if you turn them both to the same state when off). In that case, you could use 2 BAT54 dual diodes.
For more drive voltage and current, you can consider using one or two (push-pull) MOSFET gate drivers which are inexpensive and designed to drive large capacitive loads. They will also shift the voltage so you can drive perhaps 60Vpp from a low voltage source. That's probably getting to the ear-piercing 100dB+ sound pressure level with good mounting and cavity design, assuming a relatively large element (20-25mm). Typical voltage rating is 30V, so that would be right at the the limit.
Just to start, try this:
simulate this circuit – Schematic created using CircuitLab
With a frequency of 1kHz-5kHz. Yes, it puts DC across the element, but it won't hurt it for some testing.
You can sweep the frequency and determine the resonant frequency of the bare element.
Incidentally, hardware PWM does not give you what you want. It will change the duty cycle with a fixed base frequency. You need to change the base frequency. Typically (it varies with the micro) this might be done with dedicated frequency generation hardware or simply by reloading a compare timer module (most PICs will do this nicely) through an interrupt. The timer directly toggles the output pin in hardware so get almost no jitter provided the interrupt service routine can reload the compare value before the next transition comes along. For a 5kHz output you have edges only every 100usec, so there is rather a lot of time to reload the compare.