There were many. Duke Ellington, Benny Goodman, Artie Shaw, Glenn Miller, and Jimmy and Tommy Dorsey.

Below are some of the bands of the 1940s.

Glenn Miller

Harry James

Jimmy Dorsey

Tommy Dorsey

Duke Elington

Benny Goodman

Ben Pollack hired them both to play in his orchestra in Los Angeles, Benny in 1925 (at the ripe old age of 16!), Glenn in 1926. Later, in the early 1930s, they both played in Red Nichols' orchestra in New York City, where they shared an apartment with other musicians including, among others, Jimmy Dorsey. http://www.jackoverton.com/articles.php

"Room 1411" has always been shown to be written by Glenn Miller and Benny Goodman. It says so on the Brunswick 78 label from 1928 and when it was re-released in the 1940s.

It should be noted that session work by a contributing musician *can be substantial enough to merit a co-writing credit, it's the actual copyright filing that reveals the originator of the material. To be completely sure, check www.loc.gov or harryfox.com to ascertain the songwriting and publishing assignment of the work.

Glenn Miller was not, however, a "contributing musician" or session player but a member of the band, Benny Goodman's Boys.

Here is a website that shows that Glenn Miller co-wrote the song:

http://www.siue.edu/lovejoylibrary/musiclistening/NRJA/collections/NRJA_records/titles_p-r.htm

Here is another website that shows that Glenn Miller was the composer:

https://www.alibris.com/search/music/track/Room%201411%20%5BMiller%20Goodman%5D

The cast of Benny Benny Yeled Ra - 2001 includes: Amnon Wolf as Benny