I called to reschedule a court date that wasn't going to fit into my schedule (and hoping the officer doesn't show up).  I was told that I will get a letter in the mail telling me what my next court date is, but that I could also show up any Wednesday prior to then and have my case heard at that time.  

Is this normal procedure?  Do I have a better chance of the officer not showing if I just show up?  Will the court automatically consider me innocent if I just show up and the officer is not there?

If its a small town Justice Court, they might very well allow that. They will not allow a disposition of the case (other than a guilty plea) without allowing the Officer  time to schedule an appearance.
Part of my standard instructions upon issuing the ticket is that the driver can contact the court to schedule a court date of their mutual conveneience if the date I've scheduled them for is not convenient for the Defendant.

There is a chance to that Wednesday, [i]every[/i] Wednesday is the officers regualr court "date" and he is always there on that day.
Several people have the misconception that rescheduling may eventually result in the officer not being there and the charges subsequently being dropped. This does work now and then. But there are a couple of things that most people do not know. As tcsd pointed out most times the court will not dismiss because the officer is not there. They will just reschedule unless the defendant has been there a few times and the officer did not show. The other is that most departments place an officers ass in a sling if he does not show up for court. When the court clerk reschedules she has a copy of the officers court dates in front of her and sets the new date for one he is already scheduled for. Courtsd and officers are not so disorganized and dumb as the public would like think. There are no "tricks" you can try that they have not seen several times before you came along.