Possibly high... If a family member develops acute bronchitis, other people living in the home are at risk of acquiring the infection. The best interventions to prevent the spread of infection include frequent hand washing as well as not sharing the same utensils, drinking glass, toothbrush, etc. The person with bronchitis needs to be treated to decrease the risk of spreading infection.
Not a bettor. Cannot give you odds, but acute bronchitis is due to viral infection in 90+% of cases, and these are quite transmissible from person to person. If you are talking about chronic bronchitis with acute exacerbations, the likelihood is minimal for transmission.