I'm starting the switch to BBEdit and was getting annoyed with the notifications for simple operations such as find & replace. Thankfully Bryn found a workaround:
If a Worksheet takes more than 0.5 seconds to complete its task, it will post a notification when it returns to idle. The minimum time to wait may be controlled via expert preference:
defaults write com.barebones.bbedit WorksheetNotificationMinimumRunTime -float [delay in seconds]
Setting this to 0 will disable the notification altogether.