All three goals came in the second half. Ruben Rochina's fortunate strike was followed up by a neat finish from Jordan Rhodes, his 13th goal for the club, and an emphatic strike from Colin Kazim-Richards.
But Bowyer is not interested in taking over on a full-time basis, despite winning for the second successive game.
"I'm just giving the club a bit more time and then we'll see what that brings and what happens to myself and Terry (McPhillips)," Bowyer said.
"We've been here a long time, myself and Terry, and we care about the club so we're just helping out as much as we can.
"We're just carrying on and we'll keep carrying on until we're told otherwise and that's all we know."
He was full of praise for the players after an eventful week that has seen Rovers sack Henning Berg following one win in his 10 games in charge.
Bowyer added: "It's been a tough couple of days but I thought the players were magnificent.
"The first half was a typical game after two games over the Christmas period. Both teams looked like they needed the half to get themselves going.
"We got a bit of a lucky goal but it seemed to give us more energy and I can't praise the players enough. They have been remarkable with their efforts and deserved the win."