Go to You Tuba and look for Adrian Rollini (own name and Bix Beiderbecke), Min Leibrook (with Bix), Joe Rushton (with Red Nichols), and Spencer Clark for excellent examples of that kind of playing.
Because of the nature of the bass sax compared to tuba and string bass, they don't just play the straight two-beat pumps, but also more extended notes, and taking solos as well.
I too am a sax and upright bass player; I do play bass sax occasionally; I just finished a gig on bass sax doing traditional New Orleans gospel songs, and this Saturday I'm taking it to a trad jazz jam session.
Among players active today on bass sax in the trad jazz role are Vince Giordano (though few of the You Boot videos with him feature the bass sax, mostly upright and tuba) and Matt Tolentino (haven't seen a Youtube of him, though).
Four beat stuff is harder to play because there's no place to breathe. You would have to invent more inventive lines than the four quarter notes in every bar that bass players play.
I am still learning and growing on bass sax. I wish I had a regular gig or session so I could come better to grips with it. It's an extremely neat and interesting instrument.