The 1928 Holton catalog states that the #27 cornet mouthpiece has a "rim on the order of the Heim model but with a little broader surface". The cup depth is 19/32" and the Heim depth is 17/32". Both of these mouthpieces would be on the deep side by today's standards. Holton listed six "regular" mouthpieces, one of which would go along with the purchase of a new cornet. The mouthpiece that came with Bix's Holton would have been a 1, 2, 6, 17, 27, or 30 with the 1 and 27 models being closest in size and fairly close to a #7A Bach.
About twenty years ago I got to spend some time with Bach #620 and Bix Shoemaker even let me take the cornet home to pull the stuck slides and jammed mouthpiece! The mouthpiece in the cornet was a Bach 7A and had been stuck in it for quite awhile as it was hard to free it without doing damage to it or especially Bix's cornet. Although Bix may have played on a Bach 7A at one time he never played on the one that was stuck in the cornet as it was made in Mt. Vernon New York where Vincent Bach moved his operation in 1953.