Phantasmal Bear says that if it becomes the target of a spell or ability that it must be sacrificed. If I played Phantasmal Bear and later in the game played a creature that gave all of my other blue creatures +1/+1, would the Bear still be sacrificed, even though the Bear wasn't 'targeted' specifically?
No, you will not have to sacrifice it. See:
114.9a Just because an object or player is being affected by a spell or ability doesn't make that object or player a target of that spell or ability. Unless that object or player is identified by the word "target" in the text of that spell or ability, or the rule for that keyword ability, it's not a target.