When is it better for a woman not to get married?

[Sayfullah]

If a woman does not have a need for marriage, and does not fear sinning as a result of abstaining from marriage, to have her time dedicated to worship and call to Islam, it is liked for her, i.e. It is rewardable, to not get married in this situation.

(The same judgement applies for a man. )

The Virgin Mary, the best woman ever, was not married.

Rabi'ah al-Adawiyah, one of the elites of this nation who was from the Salaf*, declined marriage proposals so that she could devote all her time to worshiping God. In his reference biographical book, Wafiyat al-'A'an (وفيات الأعيان), Ibn Khallikan mentioned that Mohammad Ibn Sulayman the Hashemite prince of Basra, had a daily income of eighty thousand dirham. He sent to the scholars of Basra consulting them whom woman to marry. They unanimously recommended Rabi'ah. He sent her a letter asking her to marry him. He wrote, "I make eighty thousand Dirham daily, and soon, God willing, it will be one hundred thousand. I am proposing to you. I will give you a dowry of 100 thousand dirham**, and I will give you multiples of this amount after that, answer me. " She replied to him saying, "...Not caring so much about matters related to this life gives one peace of mind and body. Wanting this life causes worry and sadness. When you receive my letter prepare your provision for the Hereafter...It does not please me to have many times as much as what God gave you, distracting me from (worshiping) Him a blink of an eye, and peace be upon you."

أما بعد فإن الزهد في الدنيا راحة القلب والبدن،) والرغبة فيها تورث الهم والحزن، فإذا أتاك كتابي فهيء زادك وقدم لمعادك، وكن وصي نفسك ولا تجعل وصيتك إلى غيرك، وصم دهرك واجعل الموت فطرك، فما يسرني أن الله خولني أضعاف ما خولك فيشغلني بك عنه طرفة عين والسلام.)

* The Salaf are those who lived in the first three centuries after the Prophet, the best centuries.
**A huge amount in today's money equivalent to millions of dollars.
Image is for what is believed to be the grave of Lady Rabi'ah in the Mountain of Olives in Jerusalem.