Here's my thought. Audio from my phone via Bluetooth. Reception at another location using Arduino and BT module. Amplification using an LM 380/384 to the speaker.
My main concern is whether it's feasible.
Feasible but not very good.
First you need a Bluetooth module that will handle audio, the cheap ones do not.
Then as the Arduino doesn't have a D/A converter you have to add one or use the poor quality 8 bit PWM.
So buying a cheap Bluetooth audio adaptor is much the best option and leave out the Arduino.