The Sheffield Independent of 23 Feb 1938 reports in quite some detail the disappearance of Mrs Rice and her husband's search for her. He managed to trace her movements. She left home at Gray Street and took a bus to Malin Bridge. The bus conductor said she seemed confused. She had been ill for some time (memory loss included).
There is no mention of Mental Asylum. It would seem that the "escape from a mental asylum" is at least an exaggeration. I suppose she could have been treated there during her illness
Unfortunately the on-line newspapers do not include Sheffield Telegraph for that period. Presumably there will be more reports in there.
Dave