How does searching a library with Planar Bridge work?
"Search" is a keyword action that is explicitly defined in the rules. Rule 701.17a says


  To search for a card in a zone, look at all cards in that zone (even if it’s a hidden zone) and find a card that matches the given description.


In the case of Planar Bridge, you look at all of the cards in your library, choose a permanent card from among them, and put it onto the battlefield.