That time period is the rut season for the buffalo. They do get cranky, go where and when the hell they want and do NOT like motorcycles. They will be on the NE corner of the park. Elk and Deer will also be active as their rut will be soon coming in a month or so.
You are dead on about the crowds. They will be greatly reduced because school has started. Do get a snack and ice cream at the lake store. They do shut down sometime in October so I'd call ahead to the Ranger Station and find out when you want to go there. I went in September last year and the weather was wonderful and the park uncrowded.