The former Parkhead goalkeeper believes the re-building programme and preparations for season 2021-22 should begin now with a new boss setting to work before the summer.
Eddie Howe is believed to be the likeliest candidate to replace Neil Lennon on a permanent basis – but his advisors have indicated the former Bournemouth coach will not make a decision on his future until the summer.
However Bonner believes it’s imperative a new broom begins sweeping at Parkhead now and implementing change for a clear run at Europe with the campaign kicking off in July.
"What are they afraid of? Tom [English]says they might not want to be tarnished what is going on at the moment, but what are you afraid of in keeping the guy until the end of the season and then announcing him?” he said on BBC Sportsound.
“I know Eddie Howe will have a say in that, but if he is the man and the decision has been made now, why not get him in now?
“The pre-season is a critical time in any manager’s season because you lay down your strategy and get the players thinking about it.
“It’s 12 weeks until the first pre-qualifying matches for Europe and you have got to get at least four to five weeks before that.
"Some players he might target could be playing in the Euros so why not now, get him in to get established?
"Forget about and write off this season and don't worry about these games. At least you're in now to do the job.”
John Kennedy has taken interim charge of Celtic since the departure of Neil Lennon in February and Dominic McKay took on the role of new chief executive at Parkhead late last month.
Howe has been among the leading names linked with the manager’s position but no announcement on the role, or on a mooted sporting director or director of football position, has been made.
Celtic lost the final Old Firm game of the season 4-1 on Sunday to fall 23 points behind Steven Gerrard’s side with two games remaining. It is the first time since 2000 Celtic have gone a season without a win over their rivals.