Jesus answers this question Himself in Luke 8:48 -
48“Daughter,” said Jesus, “your faith has healed you. Go in peace.”
We have the same thing in Matt 9:22 -
22 Jesus turned and saw her. “Take courage, daughter,” He said, “your
faith has healed you.” And the woman was cured from that very hour.
Again, in Mark 5:34 -
34 “Daughter,” said Jesus, “your faith has healed you. Go in peace and
be free of your affliction.”
The miraculous cure of the woman was healed the same way that the daughter of Jairus was healed - the power of God grasped by the "hand" of faith. Jesus effectively says to this woman who has suffered for 12 years, "your faith has healed you"; that is, if her faith had not ben enough to drive her to do something illegal under Torah law (her bleeding made her an outcast) then no healing would have occurred!
Thus, Jesus says that her actions, impelled by faith healed the woman because she reached out for the divine cure. In commenting upon the parallel passage in Matt 9:22 we have the Cambridge commentary:
- thy faith hath made thee whole] Rather, “thy faith hath saved thee,” and not the external act of touching my garment. True
faith—spiritual insight—will be accepted by Jesus in spite of
Ellicott also comments:
The teaching of the narrative lies almost on the surface. There may be
imperfect knowledge, false shame, imperfect trust, and yet if the germ
of faith be there, Christ, the Healer both of the souls and bodies of
men, recognises even the germ, and answers the longing desire of the
soul to be freed from its uncleanness. Other healers may have been
sought in vain, but it finds its way through the crowd that seems to
hinder its approach, and the “virtue” which it seeks goes forth even
from the “hem of the garment,” even through outward ordinances (for
thus we interpret the miracle, which is also a parable), which in
themselves have no healing power.