Praise be to Allaah.
A woman who does not have a mahram to travel with does not have to go for Hajj or Umrah, and she is excused if she does not go. It is haraam for her to travel for Hajj or for any other reason without a mahram, and she has to be patient until Allaah makes it easy for one of her mahrams to travel with her.
The ways of goodness are many. If a Muslim cannot do one act of worship, he may strive hard in those acts of worship that he can do, until Allaah makes it easy for him to do the acts of worship that he could not do.
By the bounty of Allaah towards His believing slaves, if a person resolves to do an act of worship but he is unable to do it because of some excuse, he will be granted the reward of one who does it. Al-Bukhaari (4423) narrated from Anas ibn Maalik (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) came back from the campaign of Tabook and when he drew close to Madeenah he said: In Madeenah there are some people who, whenever you marched or crossed a valley, were with you. They said: O Messenger of Allaah, but they were in Madeenah. He said, They were in Madeenah because some excuse kept them back.
The scholars of the Standing Committee said:
A woman who does not have a mahram does not have to do Hajj, because in her case a mahram is part of being able to do Hajj, and being able to do it is one of the conditions of Hajj being obligatory. Allaah says (interpretation of the meaning):
And Hajj (pilgrimage to Makkah) to the House (Kabah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one's conveyance, provision and residence)
[Aal Imraan 3:97]
It is not permissible for her to travel for Hajj or for any other purpose unless she is accompanied by her husband or a mahram, because of the report narrated by al-Bukhaari and Muslim from Ibn Abbaas (may Allaah be pleased with him), that he heard the Prophet (peace and blessings of Allaah be upon him) say: No man should be alone with a woman unless her mahram is present, and no woman should travel unless she has a mahram with her. A man stood up and said: O Messenger of Allaah, my wife has gone out for Hajj, and I have enlisted for such and such a campaign. He said: Go and do Hajj with your wife. This was also the view of al-Hasan, al-Nakha'i, Ahmad, Ishaaq, Ibn al-Mundhir and ashaab al-ra'i, and it is the correct view, because of the verse quoted, as well as the general meaning of the ahaadeeth which forbid a woman to travel without her husband or a mahram. Maalik, al-Shaafa'i and al-Awzaa'i held a different opinion and each of them stipulated a condition (allowing her to do that), but with no evidence. Ibn al-Mundhir said: they did not follow the apparent meaning of the hadeeth, and each of them stipulated a condition (allowing her to do that), but with no evidence.
Fataawa al-Lajnah al-Daa'imah li'l-Buhooth al-Ilmiyyah wa'l-Ifta', 11/90, 91
And they said:
If the situation is as described - that it is not easy for your husband or a mahram of yours to travel with you to perform the obligation of Hajj - then you are not obliged to do it so long as this is the case, because the accompaniment of your husband or mahram on the journey for Hajj is one of the conditions of Hajj being obligatory for you. It is haraam for you to travel for Hajj or for any other purpose without that, even if you go with your brother's wife and a group of women, according to the correct scholarly view, because the Prophet (peace and blessings of Allaah be upon him) said, No woman should travel except with a mahram. (Saheeh - agreed upon). That is unless your brother also travels with his wife, in which case it is permissible to travel with him, because he is a mahram for you. Strive to do righteous deeds that do not need you to travel, and be patient in the hope that Allaah will make things easier for you and enable you to go for Hajj with your husband or mahram.
Fataawa al-Lajnah al-Daa'imah li'l-Buhooth al-Ilmiyyah wa'l-Ifta', 11/96.
And Allaah knows best.