If a Jew is a virgin, is it mandatory to ask permission from her guardian before temporarily marrying her, considering that she is old enough to make her own decisions and she would otherwise fornicate with someone else?

This depends on the norm and the common law of the land, i.e. The permission of the father or the guardian of the girl (virgin) from the Ahl-ul-Kitaab is not a precondition to marriage if in their religion or in their common way of life (‘Urf) e.g. by law, it is not required for the girl to have her father/guardian’s permission for marriage.