It could also be simply for her own sadistic pleasure. Bellatrix is a deranged character. She enjoys causing pain and suffering. Hermione, being a Muggle - born witch, is an easy target for Bellatrix's hatred towards those she considers inferior. So, she might torture Hermione just because she can and because it gives her a sense of power and enjoyment.
One possible motive could be jealousy. Bellatrix is extremely loyal to Voldemort, and Hermione is a very powerful and intelligent witch from the side opposing Voldemort. Bellatrix might see Hermione as a threat and also be jealous of the attention Hermione gets from Harry and Ron. So, she tortures Hermione to try and break her spirit and prove her own superiority.
Well, Bellatrix is a very complex and cruel character. In the fanfiction context, she might torture Draco to assert her dominance. She is a powerful and deranged Death Eater, and by torturing Draco, she can show that she is in control. Also, it could be related to her pure - blood mania. If she thinks Draco is not living up to the pure - blood standards in some way, she may take it upon herself to 'correct' him through torture.
One possible motive could be Bellatrix's loyalty to Voldemort. She might think that by kidnapping Hermione, she can get information about Harry Potter and the Order of the Phoenix. Hermione is known to be very intelligent and Bellatrix could believe she has valuable knowledge. For example, Hermione might know the location of Potter or the Order's plans against Voldemort.
One reason could be pure hatred. Bellatrix despises Muggle - borns, and Hermione being a very intelligent and powerful Muggle - born would be a prime target for her wrath. Another could be jealousy. Hermione's skills and knowledge might make Bellatrix feel inferior, leading her to lash out.
Another motive could be related to Bellatrix's loyalty to Voldemort. Maybe she suspects Hermione of something, and this is her way of getting a reaction out of her. She could be trying to unnerve Hermione to see if she gives away any secrets or shows signs of being involved in something that Bellatrix or Voldemort would be interested in.
You can try fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Hermione tortured by Bellatrix' in their search bars.
It depends on how the author writes it. If it's very graphic and violent, it might not be suitable for younger readers. But some authors can handle the dark theme in a more tasteful and less disturbing way.
One possible plot could be that Bellatrix captures Hermione and tries to torture her for information about Harry. But Hermione, using her wits and some new-found powerful magic she has been secretly studying, manages to turn the tables and kill Bellatrix in self - defense.
One popular fanfiction that might include such a scene could be 'The Darkest of Bonds'. In this fic, their interactions are complex and full of tension. However, it's important to note that fanfictions vary greatly in quality and content.
Perhaps in the fanfiction, Bellatrix stabs Hermione as a way to get to Harry Potter. She might think that by harming Hermione, she can draw Harry out and into a trap. Hermione is one of Harry's closest friends, so this would be a strategic move on Bellatrix's part.
One possible motive could be revenge. Bellatrix killed Sirius, who was very dear to Harry. So in the fanfiction, Harry might be driven by the intense desire to avenge Sirius' death.