Well, she might become more vulnerable. Usually, Bonnie is full of life and always ready for an adventure. But when sick, she could be more dependent on others like Clemont. Her positive attitude might also be affected, and she could start to worry about not being able to keep up with her friends.
One possible scenario in fanfiction could be that Bonnie catches a strange illness from a new Pokemon she encounters in the Kalos region. This illness might cause her to lose her energy and enthusiasm, which are her usual traits. Her friends, Clemont and the protagonist, would then search for a cure.
It could be that Bonnie's sickness is a psychological one. Maybe she witnessed something really traumatic during a Pokemon encounter, like a powerful and cruel Pokemon attacking a weaker one. This shock made her fall ill. Ash and Clemont would try to help her overcome this trauma by taking her to peaceful places and showing her the good in the Pokemon world, hoping it will heal her mind and body.
I'm not sure of a specific one off - hand. But you could try searching on fanfiction - dedicated websites like FanFiction.net or Archive of Our Own. Just type in 'Pokemon X and Y Bonnie hurt' in their search bars, and you should be able to find some relevant stories.
Her Staryu and Starmie could use their water - based powers to cool her down if she has a fever. Psyduck might try to use its 'confused' state to make her laugh. Goldeen could swim around in a small pool near her bedside to cheer her up.
In the fanfiction, Bonnie's Pokemon might develop new abilities or behaviors due to the mermaid influence. Her Sylveon could start to communicate with the mermaids in a unique way, perhaps using its ribbons to send messages. This would make Bonnie see her Pokemon in a new light, and their relationship would grow deeper as they all adapt to this new situation together.
It could be about Shauna's journey in the Kalos region. Maybe it focuses on her interactions with the player character, her growth as a trainer, and her experiences with different Pokemon. For example, it might detail how she overcomes challenges in battles and forms deeper bonds with her Pokemon.
One possible fanfiction could be where Bonnie catches a rare Pokemon - related illness. Maybe she got it from exploring an old, mysterious forest in the Pokemon XY world. Her friends, like Ash and Clemont, would then have to search for a cure. They might visit different Pokemon Centers and ask the Nurse Joys for help, but find that this illness is something they've never seen before.
One possible fanfiction could be about Bonnie getting hurt during a Pokemon battle. Maybe she tries to protect her Pokemon and ends up getting injured herself. It could show her courage and the bond between her and her Pokemon.
One possibility could be that Calem's immortality is a result of some ancient Pokemon power. Maybe he stumbles upon a hidden temple in the Kalos region where a powerful Pokemon bestows this gift upon him. This would lead to him having to deal with the loneliness that comes with immortality as he watches his friends and family age and pass away.
His comrades would likely have to protect him more. Since he's sick, he becomes a liability in dangerous situations, so the others in the Rebels would need to step up and ensure his safety. For instance, they might have to fend off Imperial attacks while Ezra is recovering in a hidden base.