Bronchitis in itself is contagious, but, asthma is not. Asthmatic bronchitis is not a contagious condition. Asthmatic bronchitis, in itself, is not contagious. However, the condition can be contagious if the person suffering from this condition also has a pre-existing respiratory disorder. Therefore, we can say that asthmatic bronchitis can be contagious as well as non contagious, depending on the respiratory disorders that a person suffers from.