The elk mating season starts in September at the National Bison Range in Montana

From USFWS National Wildlife Refuge System:

The elk mating season starts in September at the National Bison Range in Montana, with much bugling by males as they try to attract females. You can get great views of wildlife along Mission Creek, especially in the morning or evening. Red Sleep Mountain Drive is usually open until October. Your car is a terrific observation and photography blind. The wildlife at the National Bison Range are quite acclimated to vehicles but skittish around people. The refuge closes at dark. 
About the National Bison Range:http://bit.ly/2buRk1D