The Bible has very little to say about how a believer should dress. However, believers are meant to be people who dress modestly according to 1 Timothy chapter 2 verse 9.
In the Qur’an in surah 24 Al Nur ayah 31 it states clear instructions for the conduct of Muslim women; ‘Believing women should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof: that they should draw their veils over their bosoms and not display their beauty except to their husband, their fathers, Their husbands fathers their sons their brother and their brothers sons or their sisters sons or their women or the slaves whom their right hand possess or male servants free of physical needs, or small children who have no sense of shame of sex; and that they should not strike their feet in order to draw attention to their ornaments and O ye Believers turn ye altogether towards Allâh that ye may attain bliss.’
The New Testament teaching of Paul the Apostle in 1 Corinthians 11 verses 1 – 16 states: ‘I praise you for remembering me in everything and for holding to the traditions just as I passed them on to you. But I want you to realise that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonours his head. But every woman who prays or prophesies with her head uncovered dishonours her head—it is the same as having her head shaved. For if a woman does not cover her head, she might as well have her hair cut off; but if it is a disgrace for a woman to have her hair cut off or her head shaved, then she should cover her head.
A man ought not to cover his head, since he is the image and glory of God; but woman is the glory of man. For man did not come from woman, but woman from man; neither was man created for woman, but woman for man. It is for this reason that a woman ought to have authority over her own head, because of the angels. Nevertheless, in the Lord woman is not independent of man, nor is man independent of woman. As woman came from a man, so also a man is born of woman. But everything comes from God. Judge for yourselves: Is it proper for a woman to pray to God with her head uncovered? Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, but that if a woman has long hair, it is her glory? For long hair is given to her as a covering. If anyone wants to be contentious about this, we have no other practice—nor do the churches of God. See question 111 for the Islâmic answer to this question.