In the PNW we don't grow Bermuda grass, but much finer red fescue, rye, and blue grass blend. Broad leaf weeds such as dandelions, etc are a pain. Agree that one key is healthy deep roots that will help choke out the weeds. Fertilizer high in potassium and phosphorus promote root growth vs. nitrogen that promotes leaf growth. Another key is deep enough topsoil that grass with finer roots can engulf. Weeds do better in poor soil because they often have a tap root that can go down deeper than grass roots to where water and other minerals might exist. Aerating and reseeding can be effective too. If you do have way too much weed, then a weed and feed after a year, then reseeding after waiting some time for the soil to purify might be in order. Good luck.