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Robertson impressed Bury boss Alan Knill when representing the Blades in pre-season at Gigg Lane. He netted a brace against the Lancashire outfit.
Kevin Blackwell said: "Jordan caught the eye at Gigg Lane and will do a good job for Alan Knill them with his energy and enthusiasm, but he has some experienced strikers in front of him here."
Bury are the seventh club who Jordan has joined on loan.