Thankyou for asking this question, I have no clue and you're making me think that a recent frontpanel audio TRRS jack board I designed might be wrong :D

There are two possible options I can see:

1. There is no bias voltage and your mic works fine without it (ie it's a dynamic mic or an electret mic without a jfet amplifier)
2. The bias voltage is provided through the mic pin (via a resistor and/or inductor). The mic then overlays AC onto this DC signal.

I cannot find any good references or info about mic bias and TRRS connectors :( Anyone else have any luck? Wikipedia says it's a standard referred to as "CTIA" or "AHJ" but those appear to be company names, not standard names.

My current headset uses a TRRS, but also provides an extension cable that splits into two 3.5mm TRS just like yours. I might probe it out and find out what it's doing (but that doesn't mean it's the right/universal solution).