Williams is only just coming back from injury, but Ridley will be out for around six weeks with a knee problem.
Rose has made four appearances so far this season, which all came during a loan spell with Cheltenham Town.
Last year he made 40 appearances for Yeovil, scoring once, as they won the League Two championship.
He was also selected in the left back role in last year's PFA League Two team of the season.
He is United's second arrival this week, joining Macclesfield Town midfielder Neil MacKenzie - who signed on a free transfer on Saturday following an impressive loan spell with the club.