Is there a Bluetooth TRRS Headset Adapter for Audio jack on my Chromebook?

Found a solution!

I was in the same boat and extensively researched various Bluetooth devices for a TRRS-compatible solution. Finally I found this unit, the Plantronics Pulsar 260 http://www.amazon.com/Plantronics-UPP260-Pulsar-260-Stereo/dp/B000N8P4R8

While it doesn't say TRRS anywhere, if you look at the way it works, it utilizes a 2.5mm earbud/inline mic combo, rather than the usual 3.5mm audio-only output w/ an internal mic in the hardware.

I ordered this + a 2.5mm to 3.5mm adapter, and it works great with any pair of 3.5mm earbud/mic hardware. Just ensure that the adapter you order has a 4-conductor plug - if you end up with a standard 3-conductor plug you'll lose the mic signal.

Working great for both music listening and phone calls on an iPhone 5S. As is traditionally the case with Bluetooth, music listening is not super crystal clear 100% of the time - but it's stereo and works well.