Unless you have a putting green, bermuda is not usually a great choice.
It seems to me that compost tea is your only choice. To apply compost to 4 acres would cost you $5,500. Spraying compost tea on 4 acres would cost you $5.50 for the actual tea ingredients. Tea is 1,000 times less expensive than compost. You will have to buy or build the tea maker and buy an ag sprayer. After that, tea is literally dirt cheap. Go to my website
to read up on a very clever little tea maker. You should do a spring soil drench at 20 gallons per acre and subsequent monthly spraying of 5 gallons per acre. You might want to scale up your home made tea maker based on the plans on my site.
When I bought my house the back yard was washed out. I back filled with six inches of white sand. Now it is black sand due to the organic material in it. Yes you do have to water when the grass looks wilty but if you do it right, you will eventually get to the point of watering only weekly - it can happen even in sand. All it takes is organic matter provided in the tea.