Discographical information on Bing Crosby's records with Frank Trumbauer's band, Chicago, May 1932, from the Mosaic Records boxed set of Bix Beiderbecke, Frank Trumbauer and Jack Teagarden:
Cabin in the Cotton
I’m Still Without a Sweeheart (With Summer Coming On)
Bing Crosby (vcl), Max Connett (t), Frank Trumbauer (C-ms), Gale Stout (cl, as), Harold Jones (ts), Herm Crone (p), Eddie Lang (g), Charles McConnell (b), LeRoy Buck (d), Cedric Spring (vib), Lennie Hayton (dir, arr) -- Chicago, 5/25/32
Love Me Tonight
Some of These Days
As above, but add Victor Young (arr on "Love Me Tonight") — Chicago, 5/26/32
Also, it's my understanding that this wasn't a "studio band" but was Tram's working group in Chicago at the time, with Lang added because he was touring with Bing as his accompanist.
"The Last Roundup" is from a different session in Los Angeles, September 27, 1933, listed in the four-CD Properbox set of Bing Crosby as "Bing Crosby with Lennie Hayton and His Orchestra (personnel unknown)." It was the flip side of one of Bing's greatest records, his first version of "Home on the Range," recorded at the same session.