To give you the words of Mod Emilee on the topic: She said that it's not going to be a "nuke" like last time where they launch the update and *poof* all the bots are gone. It's going to be a system that is constantly running and will be detecting and banning bots automatically using an automated system.
Jagex is having their Live Stream on Sunday about Bots and their new Anti-Bot system, so considering it is on Sunday, and RS has content updates on Tuesday, this new Anti-Botting system will be turned on (in addition with Botany Bay) either on next Tuesday, or the last Tuesday of the month.
This would mean either Sept 18th or 25th if Jagex releases it along with their normal content updates (which since Botany Bay is content, it should be).
Don't expect botting to stop, expect the numbers of bots to start diminishing. This will probably mean a relatively slow market improvement instead of a rapid one like the first Bot Nuke in October.