Bowyer, who finished his stint as caretaker manager on Friday night with an unbeaten record of three wins and a draw, will hand over the reigns to Appleton on Monday morning when the former Portsmouth and Blackpool boss takes charge for the first time.
Appleton put pen-to-paper on a two-and-a-half year deal to be the new Rovers boss on Friday evening and immediately got in touch with Bowyer.
"He gave me a call before kick-off and just wished us all the best and we agreed to pick it up again on Monday," said Bowyer.
"I think he is inheriting a bunch of players with a good spirit, good character and a fantastic work ethic at the moment and they've got to continue that.
"He brings a wealth of experience, stability is needed at the football club and I think Michael will bring that.
"He's managed in the Premier League and he's been under some great managers and with the experience that he has got we'll be looking to kick on that is for sure.
"They're a great bunch of players, they've got a mix of everything. Battling qualities, skill and lots of goals in the team. The players have stepped up and taken responsibility themselves.
"They've realised that the level of performance wasn't up to the standard that they can produce and over the last four games they've produced that standard.
"They have got to maintain that now."
Bowyer has been delighted with the reaction he has received from supporters and took time after the final whistle at Molineux to go over to the travelling fans to show his appreciation.
"I've had a lot of good wishes from people over the world which is surprising," added Bowyer.
"Hearing your name sung is an appreciation from them, so I thought it was right for me to go over and thank them for their kind wishes.
"They've been through a lot and I can only thank them for their support for the players that they have given and long may that continue."
For Appleton and the first team, they've a match against Charlton Athletic at Ewood Park this Saturday to prepare for. As for Bowyer, his Reserve side kick off the second half of their season at home to Everton at Leigh Sports Village this Monday night.