Menstruation does not prevent a woman from entering ihram or performing the vast majority of Hajj's rites — it only prevents tawaf, since ritual purity is required for it. Aisha (may Allah be pleased with her) began menstruating during Hajj and was distressed, fearing she would be unable to complete the pilgrimage. The Prophet ﷺ reassured her: "Do everything the pilgrims do, but do not perform tawaf around the Kaaba until you are pure" (Sahih al-Bukhari 305).
This means a menstruating woman still makes the intention for Hajj, wears/observes ihram, stands at Arafah, spends the night at Muzdalifah, and stones the Jamarat as normal — only tawaf (and the two rak'ahs after it) must wait until her bleeding ends and she has purified herself. Scholars differ on sa'i specifically: many hold it also requires purity since it follows tawaf, while others (including Hanafi jurists) permit it without wudu since sa'i itself has no purity requirement. Where a period continues until departure, tawaf al-wada (the farewell tawaf) is waived for her by scholarly consensus, out of the same principle of removing hardship.