They have a sibling-like bond and they are the best of friends. Ibuki befriended Kokichi just by being her energetic positive, but caring and understanding self. She understood why Kokichi lied so much off the bat, she didn't know why she did, she just did. And Ibuki let Kokichi warm up to her in his own time. The first time Kokichi saw Ibuki he knew he had to befriend her. I mean, who wouldn't want to befriend Ibuki? 

They love pulling pranks on each other and other people, Kokichi supports Mioda and her metal/screamo career, they put on wacky outfits together, play games together, sing together, vent to each other, but most importantly, they trust each other and have fun together. So, yeah, they have a bomb-ass friendship.