Башкирская женщина «составляет узоры в своей голове», «это вечная, неустанная работница, является хранительницей искусства и красоты своего народа», писал русский этнограф М.А.Круковский («Южный Урал. Путевые очерки», 1909 г.).

Вот мой вариант
The Bashkir woman “makes up the patterns in her head”, “she is an eternal, tireless worker, the guardian of the art and beauty of her people,” the Russian ethnographer M.A. Krukovsky wrote in his book “The South Urals. Travel Essays” in 1909.

Если есть ошибки,исправьте пожалуйста.

'Bashkir women “make up the patterns in their heads”, “they are eternal, tireless workers, the guardians of the art and beauty of their people”......'

2. Minor point: titles of books/publications shouldn't be in double quotation marks. You have a choice of three styles in English:

No punctuation:
   The South Urals. Travel Essays
Single quotation marks:
   'The South Urals. Travel Essays'
Italics:
   The South Urals. Travel Essays

There's no difference between these three; it just depends on which style you/your customer prefers. Double quotation marks are normally used only for quotations – things people have either said, or written in books/essays/publications etc, not their titles.