From the age of eight, Bury was a lifelong philatelist. She searched for rarities, collecting letters and envelopes connected to scandals or notorious events of the 19th century. She always kept her collection to hand, never in a bank vault or safe, so that she could work on it at any time. For her knowledge, she was elected a fellow of the Royal Philatelic Society London. Bury owned a number of the rarest stamps in the world. When Sotheby's put her collection up for sale after her death, they described it as the finest collection to be sold in more than 25 years, and possibly the finest ever to have been amassed by a woman. Her collection ran to tens of thousands of stamps, with examples of every Penny Black produced including an unissued Penny Black from April 1840, and one from the first day postage stamps were officially used, 6 May 1840. In total her collection sold for £3,045,924 in 2,185 lots.
