Is inviting female teachers who do not wear the hijab—one of whom is Shiite—and gifting them Islamic books, considered a form of bribery, and how can they be invited to adhere to the hijab and follow the correct Sunnah?

Advising teachers, enjoining good, and forbidding evil to them is praiseworthy. However, gifting them religious books can be dispensed with, as a precaution for the faith, and to avoid any suspicion of bribery or undue influence, especially since they hold positions of authority which might lead them to favoritism. The books could be borrowed, read, and returned, to ensure they are read and to open avenues for discussion. If you wish to gift them books, let it be after their term of authority has ended, or with the help of other righteous sisters.