How high does your fever have to be to need an antibiotic when you have bronchitis?

High... Typically, bacterial bronchitis patients have a higher fever than viral bronchitis patients. Although there can be overlap, a fever of at least 100.5 (and usually it is higher than this!) would need to be present to say that, more likely than not, bacterial bronchitis is present.
Fever... ...Is among the least important factors to consider in deciding whether to prescribe an antibiotic or not. What is actually happening in the lungs is far more important, and we find that out on physical exam and, sometimes, xray.