This problem just recently started and after several fluhes the water is drained from the trap in the bathtub drain and we get sewer gas. The toilet is about 5-6 feet from the toilet.
This is in a 50 year old house, but the bathroom was up dated over 10 years ago.

Gurgles indicates blocked vent. The system's attempting to vent through the tub trap and is lowering the trap seal allowing sewer gas to escape. Snake the lavatory roof vent or if you think it froze up pour boiling water down it.
Since this cold snap I've been getting complaints about frozen water pipes and roof vents. Blockage or iced up the vent has to be cleared. Good luck, Tom