Now use a tongue-cleaner to scrap clean the tongue and then rinse and gargle well with mouthwash. Then try again and smell. Right-away you will become a firm believer. It helps a little and only for a very short time. The efficacy of chewing gum is probably due to the effect of stimulated saliva flow.
Prolonged chewing can get stomach all excited and prepared for food when really none is forthcoming.
The best compromise appears to be to choose only sugarless gum and to chew gum only for a minute or two at a time. The best time is to chew during the brief visit to washroom and to abandon it just before leaving the washroom. Mouth-sprays and regular mint candies are relatively ineffective in fighting bad breath. Sprays contain high concentration of alcohol. Alcohol is a good deodorant, however it can dry up your mouth intensifying bad breath.