Well, it showed up on the online-payment system at okc.gov earlier this week, and I duly paid it; yesterday the actual bill showed up.
Of interest: the time elapsed between meter readings was nearly six weeks (23 June to 3 August). Usage was what I might have expected for a month and a half. And the due date is the 11th.
Still unknown: if this is due to a change in the billing cycle, or just a temporary glitch; whether this has anything to do with the new $3.65 charge for ambulance service.