Sakura may rely on her hidden strength. If she has been secretly training a new jutsu or has some sort of hidden power, this could be the time to use it. She could unleash it and overpower Orochimaru or at least create enough chaos to break free from his captivity.
She could also pretend to cooperate with Orochimaru at first. Gain his trust a little bit and then when he least expects it, make her move. Maybe she could ask Orochimaru for some tools or access to certain areas under the pretense of helping him with his work, but in reality, she is setting up her escape.
Sakura could use her medical ninjutsu skills to create a distraction. For instance, she might make it seem like she's poisoned herself, causing Sasuke (or whoever is involved in the kidnapping) to get closer, and then she could attack and escape.
They could use their ninja skills. Sasuke might use his Sharingan to find weaknesses in their captors' defenses, and Sakura could use her superhuman strength to break through any physical barriers. Maybe they work together to create a diversion and then make a run for it.
In such a fanfiction, Sakura might be used by Orochimaru for his experiments. He could be interested in her chakra or her medical knowledge. Maybe he would try to extract some special power from her or force her to assist him in his unethical research.
Sakura can resist Orochimaru's influence through her strong will. She has always been a determined character in the Naruto series. Her love for her friends and her village could serve as a powerful motivation to not give in to Orochimaru. She could also use her medical ninjutsu skills. Maybe she could develop a way to counteract any mind - altering substances or jutsu that Orochimaru uses on her. Another way is by relying on her own combat skills. If she can keep Orochimaru at bay physically, she has a better chance of avoiding his psychological and physical manipulations.
Sakura could react with fear at first. After all, Orochimaru is a very dangerous and unpredictable character. But then she might gather her courage and try to use her strength to break free. She could use her punches, which are quite powerful, to hit Orochimaru's snake body.
Her character could develop in a way that she becomes more independent. In the fanfiction, away from the protection of her usual teammates, she has to fend for herself among Orochimaru's minions. This would force her to rely on her own strength and intelligence. Also, she might develop a darker side. Being around Orochimaru's evil influence, she could struggle with maintaining her positive outlook and might have moments where she is tempted by the power he offers without considering the consequences.
Sakura might have a hidden jutsu or power that she has not yet fully explored. In this dire situation, she could tap into this unknown ability to break free from the snakes. For example, she could have some latent chakra - based power that she discovers can repel or dissolve the snakes binding her.
Well, in such a fanfiction, Sakura being Orochimaru's apprentice could lead to some really interesting character developments. For one, Sakura would likely gain a darker and more ruthless edge to her skills. Orochimaru is known for his unethical experiments and dark jutsu. Sakura might learn some unique medical ninjutsu from him that goes against the normal ethical boundaries in the ninja world. It could also put her in a conflicted position with her former teammates, especially Naruto and Sasuke. They might view her new association with suspicion and it would create a lot of drama and tension in the story.
Sakura would probably be initially shocked and angry. She has always cared about Sasuke, and this betrayal would hit her hard. But she is also a strong - willed ninja. So, she would quickly gather her wits and start looking for ways to escape. She might try to use her knowledge of Sasuke's fighting style against him if she gets the chance.
Orochimaru is cunning and power - hungry. Sakura is strong - willed and intelligent. Their personalities would clash immediately. Orochimaru might try to manipulate Sakura, using her desires to be stronger or her loyalty to her friends against her. Sakura, though, would not be easily swayed. She would see through his tricks and call him out on his devious behavior. However, she might also be intrigued by his knowledge and power, which could create an internal struggle within her.