I had a listen to both the GRP/Decca (the "Legendary Years" box set) and the Jonzo Vol. 9 remasters of this song. I don't think that the alto saxophonist playing the call and response section is Jimmy Dorsey. Based on hearing Arnold Brilhart's lead alto work with Roger Wolfe Kahn, it doesn't sound like him either. Could be Bennie Krueger as the approach seems a little more in the Rudy Wiedoeft vein which is what I associate with Krueger's playing on the 1920 ODJB recordings.
I think I hear piano but very faintly. There's a spot, just after Bing sings "and each kiss and inspiration..." where I can hear some upper register chords, played in a descending sequence that sound like a piano. If there is piano, whoever it is was far from the mic and buried in the balance by the tuba and other rhythm section instruments.
It's a great performance, very heated compared to Bing's later version of the song. He was perfect singer to interpret Carmichael's music tribute to Bix and Louis Amstrong. The 2 different transfers were interesting to compare. The GRP/Decca being "harder" sounding with more surface noise but more detail in the higher frequencies and the Jonzo, much warmer with a bit of loss of the high frequencies.
Thanks, Albert, for starting an interesting thread!