Though the SS+ (3830) store page's summary device specs incorrectly lists BT support, the actual BT support pages indicate correctly otherwise - there is no BT support for the SS+ (3830), though an older version of one of the support pages also incorrectly listed the 2 newer Stick models a few moths ago.
However, the Ultra (4800/4802/4850) and Ultra LT do have BT audio output (and input) support, though it may or may not connect/work with your BT gear depending on version/profiles/etc (you'd have to buy one and test the pairing/connection).
Otherwise as Strega2​ suggested you could/should get an HDMI audio extractor - there are many versions of these available including with analog RCA outputs @ Amazon/etc for as little as $15-20 or more (if thats your desire).
