Does POA stand if the person with POA gave me a bike of the person she represented and the person who they represented wants bike back?

The first issue is whether the written terms of the POA authorized her to make gifts. If it doesn't then the person with the POA (the attorney-in-fact had no authority to give you the bike and you'll have to give it back. The next issue is by "bike" do you mean motorcycle or bicycle? It actually makes a difference. A motorcycle has a title, in order to make a gift of a motorcycle, the attorney-in-fact needed to sign the title over to you. If you got the title, the bike is yours. A bicycle doesn't have a title, in order to make a gift of a bicycle, the attorney-in-fact needed to give you possession of the bicycle along with saying (or better writing) that's it's a gift. Of course, as with every legal question, I'm assuming that you weren't holding the attorney-in-fact at gunpoint or you didn't con her by claiming to collecting for a charity or something.