A couple of ideas...
Using an H-bridge to drive both sides of the transducer will double your effective swing available from your supply.
A square wave oscillator that’s filtered with an L-C low-pass will give you roughly the waveform you need.
Such a thing could be constructed from CMOS buffer logic, including the oscillator. With both-sides drive it would happily work on 5V, which means you could power it from USB.