Bush, a 10-year NFL veteran, is also considered a more reliable option at Hayne's other position, running back.
Against the Seahawks Bush took a conservative approach to the punt return job, letting two punts bounce, called a fair catch on another and his only return was for nine yards.
McGaughey said the punt return unit needed to do a better job blocking to give Bush room to move.
The 49ers have lost five of their seven games and play away against the three win, three loss division rival St Louis Rams on Sunday.
49ers quarterback Colin Kaepernick and coach Jim Tomsula on Wednesday attempted to shoot down reports about locker room animosity toward Kaepernick.
A weekend news report described out-of-form Kaepernick as being on an "island", isolated by team-mates.
"No, I have a great relationship with my team-mates," Kaepernick, who questioned the credibility of the source of the story, said.
A year ago the team was also hounded by locker room rumours about then coach Jim Harbaugh's standing with the team, which ultimately ended with him leaving the club.
"I really hope not," Kaepernick, asked if he was concerned about being this year's scapegoat, said.
"I give everything I can to this organisation."
-AAP