How can I perform Umrah without a mahram, given my husband's busy schedule and inability to accompany me for an extended period?

A woman who does not find a mahram (definition) to travel with her is not obligated to perform Hajj or Umrah (definition). She is excused for not undertaking it, and it is impermissible for her to travel for Hajj or anything else without a mahram. She must be patient until Allah facilitates one of her mahrams to travel with her. If a servant resolves to perform an act of obedience but an excuse prevents him from doing so, he is rewarded as if he had performed it.