What does a woman do if she intended Hajj or Umrah and then started her menstrual cycle prior to reaching the Meeqat?

She should enter the state of Ihram before the Meeqat even if she is menstruating and her Ihram will then commence. This is supported by the saying of the Prophet (ﷺ) to Asma’ Bint U’mays (wife of Abu Bakr) when she gave birth and asked him (ﷺ) how she should enter the state of Ihram. He (ﷺ) said: “Perform Ghusl, wear protective padding to protect herself from menstrual bleeding, then enter the state of Ihram.”