From what I have learnt with my own DS, and good old interweb searching, along with my doctor's input, the bronchodilator (ventolin) is useful for opening the airways, it is to relieve the symptoms, but is not a 'cure'. Bronchitis in it's acute stage is caused by a virus, and so all one can do is relieve the symptoms. It usually clears itself up/is self limiting.
The steroid inhaler is usually only be prescribed or used for chronic, ongoing bronchitis where all other treatment has been unsuccessful. Google bronchitis + children + steroid inhaler or + treatment.
My DS was prescribed these same medications @ 9mths for what my original doc said was 'a wheeze' possibly asthma, after ongoing bronchitis, I, like you refused to give steroids of ANY dose without a second opinion and further independent research. Subsequent tests revealed the wheeze and cough was due to a combination of food intolerances. A couple of months with no wheat, potato, MSG and sodium nitrate, and he has never looked back.
I personally never commenced with the steroid inhaher, however did use the ventolin for several days over the worst of the coughing. I have since found a humidifier and lots of drinks to be just as effective as the ventolin. I do not continue to medicate my child when I am unsure of the necessity of that medication, just because a doctor said so unless I know that I don't have any alternatives, and the medication is essential.
Get googling!!! And good luck.