If your character already has a familiar, but isn't a pure caster (Such as Eldritch Knight) do they have to take Familiar Bond to get to Improved Familiar Bond? Or do they bypass the initial feat requirement by virtue of already possessing the familiar?
You need Familiar Bond for Improved Familiar Bond.
If you already have a familiar and have Familiar Bond, you either use your class level (in the class that granted you the familiar) or your character level to determine your effective wizard level. However, if you do the latter, you don't gain any special abilities.
With Improved Familiar Bond, you treat your character level as your wizard level and gain all of the special abilities.
That being said, I think most GMs wouldn't mind letting you take Improved Familiar Bond as an Eldritch Knight. The familiar's special abilities aren't worth losing two feats for.