If you already have a $dbh open in your app, then pass it in to all the methods instead of passing it into the object's constructor. Why should the object know about the $dbh if you don't ever want to serialize it?
My criteria for good software:
Does it work?
Can someone else come in, make a change, and be reasonably certain no bugs were introduced?
Re^5: Never use Storable to save XS objects