How do you respond to bonjour mon amie?

Just a plain "bonjour", nobody uses "mon ami" or "mon amie" in France anymore than "hello, my friend" is used in English.

For a speaker from France, "mon ami" is one of the clichés used to parody an overly friendly French speaker from one of the former French colonies in Africa, so it could have a slight racist connotation.

Regardless, it is not used to greet a loved one either, so stick to "bonjour", maybe followed by the person's first name, since (s)he seems to be familiar enough to call you "mon amie".