If you're just recovering from bronchitis, I don't recommend that you run either. Your immune system is still in a weakened state. If you try to run, you risk running your body down and getting sick again.
If you feel like you have a bit of energy, start with a daily walk. If you feel up to it, you can add some brisk walking during those walks. Slowly ease back into your exercise. Don't try to do too much too soon because you don't want to get sick again. That's happened to me enough times that I finally know better.
When the cough is gone, then you can think about running. but if you're kinda iffy, take a walk. And keep pushing the warm fluids like tea or soup. the dry winter air could aggravate the cough.