Luckily, Lily and August help us out with this one. August asserts that:
Most people don't have any idea about all the complicated life going on inside a hive. Bees have a secret life we don't know anything about. (8.89)
Lily finds this idea really groovy, because she sees parallels with her own life:
I loved the idea of bees having a secret life, just like the one I was living. (8.89)
No, she's not saying that the bees are runaways or fugitives from justice like she and Rosaleen are, so what is going on here?
Well, in the case of the bees, the "secret life" encompasses all the complexity of life "inside a hive" that no one gets to see. Of course, we don't have to look far to find an analogy in Lily's circumstances; she has a whole complex inner life that she keeps hidden away from other people. So, it's not "secret" in the sense of being subterfuge; it's just private, which, Lily seems to think here, can be kind of a wonderful and special thing.