although Почему бы нет? is not that uncommon, i'd say that the form Почему бы и нет? is more frequent and sounds more complete

i'm afraid i can't give a logical explanation, but you may as well say А почему нет? or just Почему нет?

i'd guess that since Почему бы (и) нет? expresses hypothetical possibility бы is used, because бы grammatically signifies potential mood