Why would my doctor prescribe prednisone and antibiotics for bronchitis?

Assist breathing. Bronchitis could cause a tight sensation in the chest. Prednisone is a steroid that works to open up the bronchioles. Prednsione can sometimes help to improve the tight sensation. It also helps to improve wheezing if it is heard on physical examination.
Treatment... Acute bronchitis is typically due to an infection so, if a bacterial infection is the etiology, antibiotics would be prescribed. And, if you have bronchospasm or airway inflammation from the bronchitis, steroids are used to decrease airway inflammation and resolve bronchospasm.