The Search discussion

There was this book I read quite some time ago and I'd love to find it again.

In this book, humans seem to die at the early age of 30-40, leaving society to the teenagers. The setting is far into the future, where some technologies have been lost, reverting to a more tribal/village living environment.
I believe the goal of the protagonist's group is to arrive at a bunker which hold either a library or a specific book.

If it helps, the first chapter depicts a runaway slave (woman) which happens upon the protagonist's village. I believe the second chapter has a battle on a bridge against the group seeking out the slave woman.

Any help with this would be greatly appreciated.