Connecting a Bluetooth subwoofer to HiFi

Is this in any way possible without modding the sub?

I have a JBL SB400 sound bar which has its own massive subwoofer, which connects via Bluetooth only, no RCA Jacks.

I've done a fair bit of googling but not found much.

Is there any gadget which can get a Bluetooth signal to this sub from my HiFi?

My kit: Cambridge A5 amplifier Pro-ject Elemental Pro-ject Phono Box

Thanks.

Sorry if this has been asked a billion times (I did a search).