I was diagnosed with asthmatic bronchitis and was wondering how long does it last, also is it normal to cough up blood with it, had this for 4 weeks?

Blood is not normal: If you have an underlying diagnosis of asthma it can sometimes flare and be called bronchitis - which is inflammation of the airways. It can last from 7-14 days depending on which medications you are taking to relieve the symptoms and how severe your symptoms are. It is not common to be coughing up blood. I would definitely be evaluated by a physician if this continues or worsens.