Depends on the pressure and weather.
In low pressured areas I have heard them going nuts as early as Labor day weekend. Also if you get a cold snap early it will increase bugling activity. In high pressure areas the last week of the month is probably the best for hearing bugling activity. Which makes bulls easier to locate but not necessarily the best time to call one in. It generally takes an experienced hunter with a bag of tricks to call in a big bull at this time of year after they have already gathered their cows.

Just because you do not hear bugling activity does not mean the rutting activity is not still going on.

I think the first week of September is your best chance to call in a big bull, also a very good time to find an active wallow with some cover around it and sit on it after mid morning.
The big bulls tend to gather their cows first and tend to come in silent to cow calling early in the month. Later in the 3rd and 4th weeks the big bulls have generally already gathered their cows and are more often than not likely to head the other way when confronted with bugling.

Seems to me the peak bugling period has been moving more into October here recently. The last two years they were still bugling quite heavy in my area in Idaho on the opening day of rifle season on Oct. 15th.