Is "Boogie Woogie Bugle Boy" in the public domain?

No.

According to Wikipedia, "The song was written by Don Raye and Hughie Prince, and was recorded at Decca's Hollywood studios on January 2, 1941."

https://en.wikipedia.org/wiki/Boogie_Woogie_Bugle_...

In most countries, the copyright in a song endures for at least 50 years (sometimes 70+) after the death of the last surviving composer. Don Raye died in 1985, so the earliest the song could enter the public domain is in 2036.

American copyright law is a bit more complicated when it comes to works published in the mid-20th century, but suffice it to say, it's *very* likely that the copyright on this song was properly registered and renewed, and hence it is *very* likely that it remains under copyright protection in the United States.

http://copyright.cornell.edu/resources/publicdomai...

I believe the copyright expires in 2036.