Used baking soda a vinegar to clean drain, but smell continues to be present. Read that I should have the air vent checked to see if it's clogged, but I get no smell from the other shower leading me to think it's just the gas backing up from the pipes. Also, how does an air vent get clogged? Anyway, another suggestion is to pour a gallon of bleach into to shower drain and follow-up with hot water the next morning. If the contractor had put in a u-trap, I know the smell would not be an issue but the problem exists and ripping up the floor is not an option.

"if the plumber had put in a U trap". If the plumber didn't put in a "p" trap he made a major code violation. You could also have a vent clog in a vent or stack and the water flow from the toilet flushing pulls the trap dry or no vent for the shower.