Ai was raised a scientist in a strict and secretive household. Her interactions with the Org has jaded her. However, throughout the series we're shown Ai actually has very girlish hobbies and tastes.
Aiyumi is just the kind of person who could reach out to Haibara. It has been shown that Aiyumi is probably the person closest to Ai anyway. Aiyumi is probably the only person Ai has never made a snarky comment to in her friend group.