That is a very interesting question. The simple answer is that it probably only saves $10-20/month max.
However, if you allow the internal temperature of the water heater to get too cold too often, it can lead to risks like mold growth or other contaminants.
I'd suggest looking into a tankless water heating option, which would only use energy when hot water is demanded, so you wouldn't need to deal with switching it on and off.
If a new water heater isn't desired or is beyond what you would like to budget, then I would highly recommend you call a local plumbing company to discuss this strategy as they will be more aware of local considerations. Another strategy would be to visit www.bpi.org and search for a local Accredited Contractor, who will likely be trained in great detail about this subject and/or able to provide reference to a reputable local plumber.
For more information:
Read "Can I save energy by turning my gas water heater down when I don't need it? Is there a timer for a gas water heater?" a Q&A answered by David Willson.