Can bronchitis be caught from a grocery store or mall?

Yes. I agree with dr. Carroll. Infectious forms of bronchitis are transmitted via airborne particles. This would be especially prevalent in situations where the air is recirculated. Airplanes, closed buildings, etc. Would be examples of this situation. I always get concerned when one passenger in an airplane is coughing because 70-80% of the air in a plane is recirculated.
Yes. As most forms of bronchitis tend to be of an infectious cause, anywhere you might pick up infections, such as stores, etc., can make you prone to picking up any respiratory illness.
Yes... Acute bronchitis is usually due to infection in the airways. If a person with bronchitis coughs or sneezes and you inhale this, you could become infected with the same infection. Coughing and sneezing into your elbow helps prevent this from happening as well as frequent hand washing.