How long should I give bronchitis to go away on its own?

Acute bronchitis... Acute bronchitis can be caused by a bacterial or viral infection of the airways. If it is due to a virus, your symptoms should be improving over a 7-10 day interval. If during this time your symptoms worsen, see your doctor or if the symptoms do not completely resolve by the end of this time, see your doctor. If you develop shortness of breath or high fever, see a doctor immediately!
Days. Five to seven days is ery reasonable as there is a high chance the illness is caused by a virus during this time period rather than a bacteria.