How to find lost ipod touch that's offline. Bluetooth is still on and can connect to my headphones
Unfortunately, you can't turn on WiFi via the Bluetooth connection.  You're headset simply doesn't have the control.  Even if paired to a computer, you can't "remote control it;"  that function simply doesn't exist.

Additionally, even if you were to use Find My to locate it, the resolution would be a few meters (about 30-40 feet).  Unfortunately, it's not "sharp" enough to tell you, "it's 10 feet from you behind the couch).

You're within range, so it's not that far.  Time to start going though the furniture with a fine tooth comb.