How can I get rid of a lingering cough?

Ever since I had bronchitis a few years ago, whenever I get a cold now, i'll have a cough that lasts a whole month after my cold ends. It's a dry cough (no mucus). It's not good to keep taking cough medicine for a month. What should I do? Other people told me they get a cough for a month too so I guess it's not uncommon.