If finger is inserted and no bleeding then it means that she is not virgin?

Lack of bleeding from the insertion of a finger into a woman's vagina, does not indication she is not a virgin. The bleeding you are referring to can be caused by rupturing a woman's hymen. The hymen is a thin membrane at opening to the vagina. As far as we know now, it serves no biological purpose and some women are born without one.

The hymen can be separated from the vaginal wall during sports, by an injury or from using a tampon and sometimes it is separated for no apparent reason. Some women will experience slight bleeding when this happens, others will not. Both are perfectly normal.

During first intercourse some women will experience slight bleeding or discomfort, and others none at all, again both are normal and neither is proof of a woman's virginity.

Historically speaking the hymen was supposed to be proof of a woman's purity or virginity and in some cultures a woman was examined prior to her marriage to give her intended assurance that she had never had sexual intercourse. If the exam showed the hymen had been "ruptured" the woman would be publicity humiliated or even put to death. Depending on the culture and how highly it values virginity.