Bulk SMS App for iPhone on Schedule
You'll have far better luck doing this on Android as opposed to iOS due to restrictions on sending SMS from applications is something that's not even kosher for App Store apps AFAIK.

There are SMS providers that allow voice and SMS from the numbers - you can check out Twilio for that. Also Google Voice offers SMS to email, so your business could switch to using that and use an email program to queue the SMS for bulk delivery as required.

Sorry to give you a no answer, but there just isn't a market for this sort of app to run natively on iOS.