Bowyer signed off from his stint as caretaker boss alongside Terry McPhillips with a 1-1 draw at Wolves on Friday night, preserving his unbeaten record and ensuring he collected 10 points from a possible 12 since taking the reins from Henning Berg.
When asked what the future holds for himself, Bowyer replied: "We (he and McPhillips) knew what we were entering when we were asked to look after it. We've got a role at the club and we know what our role is, developing players. That is the role we will go back to, both myself and Terry with the Under-18s. We'll continue to do that."
Appleton's switch from Blackpool to Lancashire rivals Rovers on a two-and-a-half-year deal was finally confirmed just two hours prior to kick-off, meaning he was not in attendance in the Black Country and instead watched the televised fixture.
Bowyer revealed Appleton called him before kick-off to send his best wishes, with Rovers' coaching staff, including new assistant Ashley Westwood, due to meet together on Monday.
Speaking about Appleton's appointment, Bowyer added: "We're delighted we've got a manager coming in who can provide us with some stability and he's worked under several good managers as well. He's a good coach, I know that from his youth days when he was in charge at West Brom. We're looking forward to working with him."
Bowyer was heading towards a remarkable 100% record after Jordan Rhodes' contentious first-half penalty - his 14th goal in Rovers colours - handed the visitors the lead. But Roger Johnson nodded home in the 74th minute to level matters and ensure both sides rightfully finished with a point apiece from an entertaining encounter.
As one era finished and another started for Blackburn, it was the same for Wanderers as Dean Saunders wrote the first chapter in his reign having been appointed as Stale Solbakken's successor on Monday.
And Saunders felt his side were worthy of all three points, saying: "I couldn't have asked for any more really. I thought we played really well. We had four or five chances in the first half. I think they had one attack after half an hour.
"Second half I thought we pinned them in again, they broke out a couple of times but never really troubled us. The spirit was outstanding from everybody, that's what I want and that's what the supporters want."