Some folks have said that Homer’s use of “bite the dust” doesn’t count because it wasn’t written in English, or depends on translations. To them we say: Check the dictionary for the origins of “nitpicker.”
As for other dust-biters, or instances of people biting dust, western civilization’s literary corpus has a whole bunch for us. The King James version of the Bible mentions in Psalms 72:9 (per Bible Gateway) that David prayed, “They that dwell in the wilderness shall bow before him; and his enemies shall lick the dust.” Not quite biting, yes. But related to the mouth and also dust? Check.
Quite a bit later, in 1750, Scottish author Tobias Smollett used the phrase when he translated Alain-Rene Lesage’s “Adventures of Gil Blas of Santillane,” as the website Writing Explained relates. “We made two of them bite the dust, and the others betake themselves to flight,” Smollett wrote (though that’s a translation from the original French). It definitely sounds like two dudes were ignobly murdered — bit the dust — and some other ones ran away.
As a thread on Quora discusses, “bite the dust” also was popularly used in TV Westerns and in shows featuring old-timey 1920s gangsters. It’s not too hard to imagine “bite the dust” being spoken by Arnold Schwarzenegger, a one-liner a guy with a gun might say to a corpse. All in all, the phrase was in popular circulation long before Freddie Mercury.