No, because aid another out of your turn requires you threatening the enemy square.
Aid another requires you being in position to perform a melee attack against the enemy, which when not in your turn requires being able to perform an attack of opportunity. You need to threaten the enemy square to perform an attack of opportunity.
Whips do not threaten the area where they have reach, and threatening is a requirement for attacks of opportunity. Thus you cannot use Bodyguard with a whip unless you have a special feat or effect that allows you to threaten with that kind of weapon (as for example the Improved Whip Mastery feat) or somehow being able to use the whip as an immediate action.
There is an specific FAQ that clarifies this:
Bodyguard: The Bodyguard feat says that I can spend one of my attacks of opportunity to aid another the AC of an adjacent ally, but it doesn’t say one way or the other whether this removes other restrictions on aid another? Particularly, do I need to threaten the attacking enemy? Also, has that enemy provoked an attack of opportunity from me?
You still need to fulfill all requirements of aid another, including threatening the attacking enemy. Bodyguard uses up one of your attacks of opportunity for the round, but the enemy hasn’t provoked an attack of opportunity from you, nor are you making one (which is relevant for abilities like Paired Opportunist).
Bold emphasis mine.