Is the misdemeanor a civil charge, or a criminal one?
If it is a criminal one then the US Constitution’s 6’th Amendment applies: “In *all* criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury [...]”
If it was a civil charge, then is the fine —or even jail-time which would be spent in employment, IIRC— more than $20?
If that’s the case then the 7th Amendment applies: “In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved [...]”
The term $20 probably refers to the value of a $20 gold piece, not the value of a $20 Federal Reserve Note; that amount is sometimes exceeded by civil fines, but not usually.