You probably need a Bluetooth capable AVR/Receiver.
In general terms, an AVR (Audio Video Receiver) is a brain box that processes both audio and video signals that you feed into it, then moves those signals to the appropriate output. AVR have built in amplifiers. In most cases there is no need for external amplification.
An amplifier is simply that. It is a power source that connects to either an AVR via the pre outs, or to an AVP (Audio Video Pre processor) that has no internal amplifiers to power your speakers.
In either case, as I said you simply need an AVR that is Bluetooth capable to connect to your control box, so that you can stream music to the AVR, and through the control box to your speakers.