Superman is currently 25. In the Golden Age, Batman and Superman were at least 3 years apart. In the Silver Age, they were about 5 years apart. In the Post-Crisis Universe, they were the same age.
But if we give some sort of gap, make them about 5 years apart, then ti works out pretty well. Batman comes onto the scene at 20 years old. During year one, he becomes the ward of Dick Grayson, who is 15 at the time of his parent's death. Sure, there's only 5 years apart, but it gives it a very "Dynamic Duo" feel in the style of B:TAS. We can even fudge it a bit and say that Dick Grayson became Bruce Wayne's ward at a much younger age.
Playing around with it further, maybe Bruce is 18 and Dick is 10. Dick becomes the ward not of Bruce, but of Alfred who takes in Dick because of the tragic way he lost his parents. When Bruce becomes Batman 2 years later, that's also when Dick becomes Robin at 12. Dick Grayson is Robin for 6 years and becomes Nightwing when he turns 18.
Concurrently, while Dick Grayson is struggling with his identity around 16 (running around with some sort of Teen Titans group), their neighbor Tim Drake (at age 14) stumbles upon their identities and insists on becoming part of the team while Bruce takes Jason Todd as the ward of the state (at age 14). Todd rushes out to be Robin first and ends up being killed by the Joker. Drake takes some time but ends up taking the mantle when his father is killed by Boomerang (Spoilers tries to do what Drake did and try to "impress' Batman in order to become Robin, but she causes a gang war and in the end she becomes a "Batgirl" along with Cassie while Barbara Gordon is recuperating).
That makes Batman 30, Nightwing 22, Tim Drake and Jason Todd 18.