Rovers put two past the visitors in as many first-half minutes, first through David Dunn after 27 minutes who danced past three challenges before tapping home and a minute later Rhodes buried a sweeping half-volley.
Alex Baptiste gave the visitors hope on the stroke of half-time with a powerful finish but Corry Evans scored a spectacular half-volley to end any thought of a comeback after 70 minutes and Rhodes bagged a second from close range seven minutes from time.
Bowyer admitted that there is some trepidation before the transfer window closes but insists Rhodes is not for sale.
"When I first took the job I asked the owners about Jordan Rhodes and they said to me that Jordan wasn't for sale, so as soon as 11pm comes on Monday, you'll all have to think of a different question," Bowyer said.
"He's better than B£10million. We paid near that figure for him and he's gone and done it in the Championship last season and he's a goalscorer.
"He's very important. He proved it again here with the quality of finishes he possesses. The first one was absolutely outstanding. It's not just his goal, it's his work rate."
Bowyer was delighted with what he described as a 'clinical' performance, after seeing his side score nine goals in a week.
He said: "We're very pleased with the goal return. I thought we were very clinical. In the first half we might have had a couple more. Their goalie has made two outstanding saves, one from Ben Marshall and the Jordan Rhodes one."