It might make things easier if you can open up a DAW and use an oscilloscope plugin on a channel assigned to the input where the mic is connected. If you take this route, make sure to also keep an eye on the input level and reduce the preamp gain so you don't clip the input / ADC
The idea is to start with "a" signal amplitude, raise it until either the top or the bottom of the sine gets clipped, adjust the bias to "unclip" it, then rinse and repeat until both the top and bottom of the test-sine get clipped at the same time, roughly by the same amount.