How can a woman achieve a legitimate marriage in Islam, given her family's faltering efforts to find her a husband?

The father should be advised to fear Allah and fulfill his duty of caring for his sons and daughters, for it is a trust he will be questioned about on the Day of Resurrection. He may offer his daughter to someone he believes to be good and righteous, as Umar ibn al-Khattab, may Allah be pleased with him, did with his daughter Hafsa. The father must realize that Islam encourages reducing the costs of marriage to facilitate it, and that obstructing young people is an invitation to corruption. "If someone whose religion and character you approve comes to you seeking marriage, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption."

As for the girl, shyness should not prevent her from speaking to her father, and she should raise her matter to Allah through supplication, for He, Glory be to Him, is too shy to turn away the hands of His servant empty and disappointed.