Blackburn 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 for the transfer window closes but insists that 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 £10 million. We paid near that figure for him and he's gone and done it in the Championship last season and he's a goal scorer.
"He's very important. He proved it again today 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 today. 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."
Bolton boss Dougie Freedman bemoaned the individual mistakes that led to the goals after watching his team slump to the bottom of the Championship. It is the first time the Trotters have failed to win any of their first five league games since 1984.
"Individual mistakes hurt us dearly. Two goals in a minute are hard to take," he said.
"I felt we got ourselves back in the game with some fight, determination and spirit to be 2-1 at half time. We've had a few opportunities in the second half to make a game of it but not taken them.
"Another individual mistake gives them a third goal and then we threw caution to the wind in the last 20 minutes with four forwards on the pitch and conceded the fourth goal so all in all disappointed with the result and the individual performance of the defending.
"I think certain players were very good today and others let themselves down. The players are hurting because they know they're better than that."
Freedman was clearly frustrated at the financial difficulties in trying to bring in new players before the transfer deadline, but conceded that he may have to do so with his team's worrying away record reading at just two wins in the previous 16 league games.
He said: "We need to try our best to recruit which is difficult. We're in a situation where we've got a lot of players on big and long contracts and we've got to try and recruit a certain type of player that shows a little bit more hunger for the football club.
"I've had to loan Marvin Sordell and Keith Andrews out for a fraction of their money to try and generate some money and I'm going to try and recycle the money.
"It's not that the money isn't there. Money has been there but it's in contracts and it's very difficult to try and reshuffle."