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. Something like the CD4050 for example: http://www.ti.com/lit/ds/schs046j/schs046j.pdf
With both-sides drive it would happily work on 5V, which means you could power it from USB. Keep in mind you can connect the buffers in parallel to boost the drive current even more.