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So far, up to Fisher lvl 21, I've found all the bait I needed for quests to be on a vendor within the main outpost for the zone you are sent to.
I don't think bait is designed to be dropped anymore. Culinarians can make a few types, but most of the others are just gotten from vendors I think.
xivdb.com has a good solid database, though not a lot of info on specific items. I suggest using it and commenting on items that you had trouble with once you find them as to help others out.
I murdered the lvl 1 rats myself... silly us for thinking a rat would drop a rat tail as loot...