There is no scripture saying one can only travel less than a mile on the Sabbath, perhaps why you didn’t provide scripture.
In the verse below a Sabbath days journey isn't speaking of a length of time but a distance of around a half a mile or so. The Jewish people practice the tradition. The Christian who stayed in the land it was a obstacle, especially traveling about.
Acts 1:12
Then returned they unto Jerusalem from the mount called Olivet, which is from Jerusalem a sabbath day's journey.