A woman who is extremely shy is sitting in a place where people are backbiting – is there any sin on her?

Praise be to Allah.

There is sin on you in that case, unless you speak out against the evil action. If they accept that from you, then praise be to Allah, otherwise you must leave them and not sit with them, because Allah says (interpretation of the meaning): 

“And when you (Muhammad) see those who engage in a false conversation about Our Verses (of the Qur’aan) by mocking at them, stay away from them till they turn to another topic. And if Shaytaan (Satan) causes you to forget, then after the remembrance sit not you in the company of those people who are the Zaalimoon (polytheists and wrongdoers)”

[al-An’aam 6:68]  

“And it has already been revealed to you in the Book (this Qur’aan) that when you hear the Verses of Allah being denied and mocked at, then sit not with them, until they engage in a talk other than that; (but if you stayed with them) certainly in that case you would be like them” [al-Nisa’ 4:140]

 And the Prophet (peace and blessings of Allah be upon him) said:  “Whoever among you sees an evil action, then let him change it with his hand (by taking action against it); if he cannot, then with his tongue (by speaking out against it); and if he cannot, then with his heart (by hating it and believing it to be wrong), and that is the weakest of faith.” (Narrated by Imam Muslim in his Saheeh). And there are many similar aayahs and ahaadeeth.