Maybe I am wrong here but I want to hunt bulls before the full blown rut is on. When they are in full rut the heard bulls have most of the cows hearded up and and are actively breeding them. They are much less likley to answer a challenge of another bull (you) or go after a lone cow (again you) when they have 20 or 30 of them that they are tending and breeding already.

I want to be in the middle of them when they are looking for hot cows, gathering up their harems, chasing after smaller bulls, and are much more likely to answer your cow and bull calls. There are a lot less eyes looking around too.