Bronchitis that has been caused due to a viral or a bacterial infection is contagious. i.e.only acute bronchitis is contagious not the chronic ones.
Therefore, it is esential to find our from your doctor whether you are or not.
Acute bronchitis is an airborne disease, so it can be spread if a normal person happens to come into contact with any body fluids from an infected person.
One more thing of interest chronic bronchitis is caused mainly from being a smoker and therefore is not contagious.