A design change to reduce the size of the hole through which gloves were retrieved could help, the study suggested.
The bacteria can cause potentially fatal hospital-acquired infections in patients.
Lead author Dr Heather Brooks, of the Department of Microbiology and Immunology, said she and her study collaborators wanted to find out whether gloves used for routine procedures could be spreading bugs.
"We wanted to find out how 'non-sterile' non-sterile actually is," she said.
World Health Organisation guidelines stipulate staff should wash their hands before using the gloves.
Gloves were likely to be contaminated when medical staff searched the dispensing box for new gloves, and their hands made contact with ones that were not selected.
It was highly likely the results would be replicated in other general wards in other hospitals, the researchers said.