how long will my Honda run with a faulty water pump?

You should make it for not long, but if you have a leak, water alone will be fine for a few days. Just keep it topped off, even if it means leaving early to fill up radiator. Just put 50/50 coolant in it when you get it replaced. No more that a few days like that though. But I don't know if when you say 'bad water pump' it's overheating, do not allow that or you will be in for $$$

If the leak is bad, I would say a mile or two maximum before your engine goes up in smoke. That is an expensive gamble with very little pay out!