Personally I would never have anyone put down Bermuda grass - it's the worst weed in the world if you're interested in gardening. Buffalo grass is adapted to the area and needs a lot less water. However, moving forward, there are things you can do in your yard any month of the year in an organic program.
The home page of DirtDoctor.com has an area in the middle for finding Organic Advice. In particular, the Organic Maintenance Calendar
and the Organic Guides
that offer a lot of answers for beginners and refreshers for the more experienced users. In particular, take a look at the enumerations of acceptable products in the organic program and the basics of organic gardening. Those should help you form a plan and come back with more targeted questions.