Could I drink alcohol now and take my antibiotic medication for my bronchitis 4 hours later?

Not a good idea. If ill with a problem such as bronchits it would be best to avoid alcohol until the full course of the medication is completed and your bronchits is fully resolved.
Depends... Some antibiotics will be ineffective if you consume alcohol while on the antibiotic. Your doctor or pharmacist can give you the particulars on the specific antibiotic you are currently taking.