Nothing seems to match exactly.
I've had a look through the "USB host" boards at Little Bird Electronics, but the only ones that have Bluetooth included are the Raspberry Pi 3. There's also the BeagleBone Black Wireless, recently announced, but not yet listed.
But Raspberry Pi 3 and BeagleBone are a bit power hungry, and given your power constraints, my guess is you'd need to go for an ARM CPU of some sort with USB host and a BLE module.
For the other USB host boards, you would have to add a Bluetooth module.