In addition to the University Six session you allude to, Brian Rust also lists Spencer Clark as the bass sax player on the California Ramblers session of August 31, 1926 - which produced "Wouldja" and "You Need Someone To Love". This was the session immediately before the one that produced "Gone Again Gal" and "She Knows Her Onions".
Spencer Clark later stated "I substituted for Adrian Rollini off and on from late 1925", so he may very well be on these sessions.
Another possibility is Jimmy Johnson, though he was a more staccato bass sax player and rather "old-fashioned" sounding by 1926, so I personally don't think it's him. Yet another name to throw into the ring is Jimmy Puglese, who Rust lists as being the bass sax player for the California Ramblers session of August 12th, 1926, which produced "How Many Times?" and "Adorable". Here is "How Many Times":-