I am sorry to hear that you are dealing with bronchitis
which, as your doctor
probably told you, is an infection of the large tubes that conduct air inside the lungs. The condition is relatively common, and it causes significant symptoms such as coughing and shortness of breath. Fortunately, the condition also usually responds quickly to antibiotics, so you should be feeling better soon.
In terms of how long you will be contagious for, most of the time after 24 hours of taking the antibiotics you should be safe to go back to work or school, as long as you are feeling up to it. However, you should check with your doctor first, as sometimes they may want you to stay home longer for other reasons.
Also, make sure to take the entire prescription of antibiotic that you were given. Stopping the prescription early, even if you are feeling better, could allows the symptoms to come back again.
Finally, although most of the time the bronchitis will clear up quickly with treatment, if you find that you are still feeling short of breath or still having significant cough even after several days on the antibiotic, you should go back to your doctor to make sure that things are improving as expected.