There is not much to do now since the bermuda will be going dormant very soon. In spring there is much to do including aerating, fertilizing, and weed control. Your county Extension Office has free information on lawn care including guidance on mowing, watering and fertilizing.
I would caution against switching to St. Augustine. Unless you wait until later in the spring to have time to spray the bermuda with weed killer a couple of times the result will be a lawn with a mixture of bermuda and St. Augustine. Again your local Extension Office can direct you to the proper products and timing if you choose to eradicate the bermuda. As an alternative, with proper care you could build a strong attractive bermuda lawn in less than one growing season.
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