The midfielder has fallen out of favour with Shrews boss Paul Simpson and has only made 12 appearances this season and none since February 21.
The Bulls are in desperate need of new players as they sit 23rd in the table, eight points adrift of safety and Pugh could make the move permanent
at the end of the season.
"Marc is down the pecking order here so the move is a good one for him," Simpson told the club's official website.
"We'll see how things do until the end of the season then take another look at it."