You are speaking of an outdoor plant? Webbing sounds more like spider mites. I use a dishsoap spray, or neem on my herbs. But, you have to keep up with it. A lot of times a good water blast can do amazing things too.

Caterpillars can produce webbing, ie, tent caterpillars. Can you see them within the webbing? JMO, but I would go ahead and use the bt. That way if the cats are gone and there is still damage and webbing you would know to suspect spider mites(which can thrive in dry environments). It shouldn't take very long to know if the bt is working, especially on small cats, but they do need to ingest some sprayed leaf to be affected.