A woman who feels shy to do da’wah
Question

How should I overcome shyness? Earlier I felt shy of even hypocrites or disbelievers. I felt sick about having them gossip about me or talk bad about me, or stare at me. I hid from them when I took up Hijaab and I realized that it was good that I didn't meet them. I didn't want to be shy of them and Allah helped me overcome that by making me know that I have to fear only Him and please only Him. Now I also feel shy sometimes about telling people the Truth. I often do not tell people who do wrong about the Quran. For instance, I often do not tell men that they should not stare at women. I feel that they may not heed my advice or I just don't want to attract their attention by talking this way with them. I also feel shy about telling other Muslim when they do something wrong. I often do not correct people person. I want them to be correct but I often feel shy. There are ways in which I do not feel shy. For instance, I do Dawah on the internet.
Praise be to Allah.May Allah reward you for your pride in your religion and your desire to call others to Allah. But you should note that a woman does not have to call men directly without a mahram, because of the fitnah (temptation) involved in that.  
We advise you, and other women, to train yourself to obey Allah and to fulfil your duties towards Allah and towards your husband, family and children. Call women to Allah as much as you can, by speaking up or by reading books or by giving useful tapes or books, or by organizing a study-circle if you have sufficient knowledge, or by speaking out if your friends do something wrong, or by offering advice to your sisters and by playing a part in helping them to solve their social problems, and so on. 
With regard to your refraining from da’wah because of shyness, this does not justify giving up da’wah, and it is a kind of blameworthy shyness. But you should note that every action that a person does may be difficult in the beginning and may make him feel shy sometimes, but if he persists in it, it will become second-nature to him, and it may reach the level that he cannot do without it. So you have to strive and be patient, because calling people to Allah, which includes enjoining that which is good and forbidding that which is evil, needs patience, as Allah says (interpretation of the meaning): 
“By Al‑‘Asr (the time).
Verily, man is in loss,
Except those who believe (in Islamic Monotheism) and do righteous good deeds, and recommend one another to the truth [i.e. order one another to perform all kinds of good deeds (Al‑Ma‘roof) which Allah has ordained, and abstain from all kinds of sins and evil deeds (Al‑Munkar) which Allah has forbidden], and recommend one another to patience (for the sufferings, harms, and injuries which one may encounter in Allah’s Cause during preaching His religion of Islamic Monotheism or Jihad)”
[al-‘Asr 103:1-3]
Patience in making da’wah is a characteristic of the believers, and is one of the means of salvation from loss, from which no one is saved but those whom Allah mentions in this soorah. They are the ones who combine four characteristics: 
1-Faith, which can only come through knowledge of Allah, His Messenger and the religion of Islam.
2-Acting upon this knowledge.
3-Calling others to this knowledge.
4-Patiently bearing any harm that comes for the sake of gaining this knowledge, acting upon it and calling others to it.
Will regard to calling people via the internet, this is something that is essential, but our advice to you and to every girl is to avoid it, because of the dangers involved, from which few are saved apart from those whom Allah protects. There are some people who have undertaken to carry out this great mission, which needs deep knowledge that will ward off doubts, and sincere faith that will ward off the influence of whims and desires. But for those who enter into this work without these two weapons or with only one of them, they are rarely safe from its pitfalls. But if you meet these two conditions then you can enter this field.
 Moreover you have done well by starting to wear hijaab, which is obligatory upon Muslim women because Allah says (interpretation of the meaning):
 
 “O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allah is Ever Oft‑Forgiving, Most Merciful”
[al-Ahzaab 33:59]
 Allah has mentioned the wisdom behind hijaab in this verse, which is to protect women against ignorant men. Praise be to Allah, the Lord of the Worlds.