Do your headphones have a 3.5mm jack? If so, you could use a bt receiver on that, make sure the receiver has multipoint.
A more difficult, but more likely to work properly, option is to get an audio interface with two inputs. Input your deck and phone into it and put a bt transmitter on the output or headphone jack. Keep in mind line-ins are usually in summed mono to you won't get directional sound.
But just to make sure I covered the obvious: could you not just play the podcast through your Deck while playing? I'm not familiar with SteamOS but Steam BPM has this option.