She made her first significant mountain ascent in 1892 when she climbed the Aiguille des Grands Charmoz in the Mont Blanc massif with Albert F. Mummery and his wife Mary. With their success, Bristow and Mary Mummery became the first women to climb the mountain. In 1893, Bristow climbed the Aiguille du Grépon—the ascent for which she was best known. This was the second-ever traverse of the Grépon, which had first been climbed by Albert Mummery two years earlier. The same year, she successfully climbed the Aiguille du Dru, the Zinalrothorn and the Matterhorn. She was known for climbing without local guides and for occasionally leading her climbing parties' ascents. Bristow's guideless ascent of the Grépon inspired Mummery to write: All mountains appear doomed to pass through three stages: An inaccessible peak, the hardest climb in the Alps, an easy day for a lady.