I had to look up where you live. I thought it was Houston.
Since the compost is down, you should be good to go. Keep the soil moist and you will grow an excellent population of beneficial microbes.
If you are going to seed bermuda HURRY UP
Common bermuda is the only one that will grow from seed and it needs HOT soil to sprout. June and July is the best time to seed bermuda.
You mentioned on another post that you were going to sod (plug) with St Aug. You can do that any time, but if you want to get it going, get going. Keep it moist and it will choke out the other grasses. St Aug will not; however, choke out broadleaf weeds. Those have to be pulled either with a Weed Hound tool or by hand.