We could not find any hadeeth with the meanings mentioned in the question or even any hadeeth that is close to it, but hijab (proper dressing of Muslim women in public) is sufficient as a virtue, as Allah, may He be glorified and exalted, has enjoined it in His Holy Book. 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.”
So the woman who covers herself is adhering to the command of Allah and obeying His law. The one who is like that is deserving of forgiveness from Allah, may He be glorified and exalted.
And Allah says (interpretation of the meaning):
“Verily, the Muslims (those who submit to Allah in Islam) men and women, the believers men and women (who believe in Islamic Monotheism), the men and the women who are obedient (to Allah), the men and women who are truthful (in their speech and deeds), the men and the women who are patient (in performing all the duties which Allah has ordered and in abstaining from all that Allah has forbidden), the men and the women who are humble (before their Lord Allah), the men and the women who give Sadaqat (i.e. Zakah and alms), the men and the women who observe Sawm (fast) (the obligatory fasting during the month of Ramadân, and the optional Nawafil fasting), the men and the women who guard their chastity (from illegal sexual acts) and the men and the women who remember Allah much with their hearts and tongues. Allah has prepared for them forgiveness and a great reward (i.e. Paradise).”
Al-‘Allamah al-Sa‘di (may Allah have mercy on him) said:
“… those who guard their chastity” means, against zina (fornication or adultery) and that which leads to it. End quote.
Tayseer al-Kareem al-Rahman, p.664
It was narrated from Sahl ibn Sa‘d (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said:
“Whoever protects that which is between his jaws and that which is between his legs will be guaranteed Paradise.”
Narrated by al-Bukhari, no.6474
There is no doubt that the woman who observes hijab completely and has the characteristics of chastity and modesty will protect herself and her honour more than the one whose hijab is lacking and who uncovers any part of her body, even if the latter also keeps away from zina and what leads to it.
Hence Allah has promised to the women who adopt complete hijab and protect their honour from haram (unlawful) things, forgiveness and a great reward, and the Prophet (peace and blessings of Allah be upon him) guaranteed that they would enter Paradise.
And Allah knows best.