Rovers edged out of the npower Championship relegation zone courtesy of back-to-back home wins over Derby and Huddersfield over the past week.
Success has been harder to come by on the road, with their last league victory coming at Barnsley in late December when Bowyer began his first spell in caretaker charge before Michael Appleton's brief stint as manager.
Bowyer said: "The Championship this season shows that anybody can beat anybody, both home and away, and that's the mindset that we'll be going with - to get on the front foot against Watford, go and put them under pressure and create the chances for the likes of Rhodesy (Jordan Rhodes) to continue his scoring run.
"We're not going to go down to Watford to make the numbers up, we're going to win.
"We've got to pick points up and that's the mindset from now until the end of the season. If it's away we can't do anything about the fixture list.
"Winning games breeds confidence. We've got back-to-back wins and we've just got to keep our feet on the ground, recover quickly and go and take the challenge on."