Ainsworth had been recalled by Watford, before being sold on to Huddersfield Town, with his loan stay with the Bulls set to end after this weekend's trip to Walsall.
That prompted United supremo Graham Turner to move for Myrie-Williams, who turned down a switch to Edgar Street earlier this season.
Myrie-Williams, 20, has spent time with both Carlisle United and Cheltenham Town this term, having spent much of last season on loan at Tranmere Rovers.
He has scored twice in 36 appearances for the Robins, but has not featured for the Ashton Gate club since April 2007.