Gene Barry was 39 when he started as Bat Masterson. In real life, Bat Masterson fought his last gun battle in 1881 at the age of 27. That gunfight took place in Dodge City.
The "derby" Gene Barry wears is incorrect. If you look at real photos of Bat Masterson you'll see that the brim on Gene's hat is too large. They tried to roll the sides more to make it seem smaller, but it still just looks like any old cowboy hat with a rounded crown.