I always figured they aged at the rate that felt right.
You know how when you were a kid you either wanted to stay one forever or grow up real fast? You had no say in the matter; your body always aged for you. Even if you remained a child at heart, you'd always grow up a little to at least adapt to world around you. Or if you wanted to grow up, you still had to wait another 10-15 years for that to actually happen.
But after you die in the Bleach world, you're sent to the Soul Society. And if you're just some random shmuck, you have no reason to age. You're dead. You're body is just made up of your soul and what little reiatsu you have; and since you have no actual physical body, you can age at a rate that feels right for you.
That's probably why people stay what- 2000 years?- before re-dying in there and being reincarnated. Most of them don't want to age past their prime and do it sloooooowly after a certain point (but they don't stop since others are aging as well and it happens unconsciously).
The same thing can be applied to the shinigami.
Byakuya grew up fast since he wanted to catch up to Yoruichi, and then stayed in his prime.
Yachiru was always safe and happy with Kenpachi, so she never felt the need to grow anymore as a child.
Yamamoto shows that people still age, so there's no getting around it in the end.
Heck, even Shrimpo could've slowed his aging since he always a child prodigy and growing up would take that away.