Bjugstad, 33, joined the Blues on a two-year, $3.5-million deal in July.
In 35 games with St. Louis this season, he recorded six goals and one assist.
Currently in his 14th NHL season, the veteran has 337 points (163 goals, 174 assists) over 795 career games.
He now heads to a fading Devils squad that has lost four of its past five games and sits second-last in the Eastern Conference with a 28-26-2 record.
Bordeleau, 24, comes back to the Blues having appeared in just 44 NHL games. This season, Bordeleau has eight points over 35 games with the AHL’s Utica Comets.
The Blues are also on the outside looking in of the playoff picture, sitting second-last in the Western Conference with a 20-27-9 record.