A burglar reached through an open window to gain access to a house in Kirtling Place, last Sunday at 4.45pm.
He unlatched a window below a fanlight, which had been left open.
Once inside the offender picked up a Bailey & Quinn brown leather handbag before being disturbed by the occupants and fleeing back out through the window, taking the bag.
Items contained in the bag included an Apple iPhone 5s and around £90 in cash.
Officers are warning residents to always ensure they have secured windows when not at home or before going to bed and to keep doors routinely locked at all times.
Anyone with information about this crime is asked to contact the Bury St Edmunds Priority Crime Team on 101 quoting reference HH/14/1585, or Crimestoppers anonymously on 0800 555 111.