Arduino to an external bluetooth speaker

I want to setup an Arduino Nano with Chenbo MAX446 Electret Microphone Amplifier Module breakout board to wirelessly connect to an external bluetooth speaker so I can use the Arduino to transmit my voice wirelessly to the bluetooth speaker and out to the masses. I plan on running this off a 9v battery with a step-down to 5v.

I am trying make the transmitter as small as possible (hence why I am using an Arduino Nano instead of an Arduino Uno). I know that I will need some type of bluetooth shield/board but which? It will be a short range to the speaker so not sure about fighting a possible feedback loop from mic to speaker as well.

Any help on hardware selection and coding would be awesome!

Bluetooth seems like a bad idea. Why not RF?

If you must.. maybe this thing?

Thank you for pointing me to the Bluetooth Audio Transmitter & Receiver Board EMBT-S02. I am liking this board from the link you sent.

This could work better than the HC-05 Wireless Bluetooth RF Transceiver that I was thinking of using.
I have a portable bluetooth speaker that i can tuck in a pocket to send the audio (voice transmission) to.

The work is in making the transmitter to send the voice transmission to the bluetooth speaker (and getting the receiver (speaker) to sync with the transmitter (nano + EMBT-502 + Max4466) system.