Ideally in spring, Bermuda needs to be scalped as low as you can go and clippings must be removed, once the grass has reached about 50% green-up. The idea is to get sunlight on the soil and warm it up to wake up the bermuda, then hit it with N to really push it to grow out.
Typically thats late March/April-ish here in N Alabama. You really want to watch the weather and how its trending to determine what and how much fert to put out. Typically I'll go light, 16-4-8 or 10-10-10 in April immediately before/after scalp, and once its 100% green I'll hammer it with 30-0-10 at 1-2lb N/1000. You really want to push it harder at this time.
Wintry grasses, no. Zoysia yes. Other summer lawn types like centipede or Ag, no.