Could tongue bleeding have anything to do with bronchitis?

Not likely: You could cough up some blood with a severe bronchitis, but bleeding from the tongue would be very unusual. If you have a sore or other spot that is bleeding anywhere in the throat, get it checked out asap, it could be a cancer.

Tongue bleeding: If the bronchitis is also causing sinus congestion and mouth breathing, then yes if your tongue is severely dried out. Try to keep your mouth moist, with either water or a salivary substitute you can get from the pharmacy. But you should have it checked out by your physician, to see if the bleeding is caused by a more serious condition.

Very unlikely: The blood that you think is coming from the tongue may be coming from coughing or spitting up blood or something in your throat. It should not cause the tongue to bleed. If in fact you have bleeding from the tongue, you most likely have something else going on. See your dentist or an oral surgeon to evaluate what's going on. I assume you are being treated for the bronchitis by your physician.