Bilbo lets you search and add a treasure card to your hand for 1 baggins resource. But it does not say to shuffle your deck after finding it. So I have not been...is that correct?
No, that is incorrect.. You always shuffle after searching a deck, even if the card does not specify it, unless the card itself explicitly says otherwise.
From the official FAQ:
(1.21) Search Effects
Whenever a player searches through a deck, that player
shuffles the deck after searching it unless a card effect
says otherwise. Players do not shuffle or change the
order of a discard pile after searching it.