Chairman Mitchell made a bold move when he took the decision to appoint the untried pair following Eddie Howe's departure to Burnley in January.
But the duo came up trumps by steering Cherries into the play-offs and will now attempt to secure back-to-back promotions for the first time in the club's history.
Bradbury and Fletcher took the reins when Cherries were in third place, immediately raising hopes of automatic promotion thanks to an impressive 10-match unbeaten run.
However, despite failing to stay with leaders Brighton, Cherries had already guaranteed a play-off semi-final against Huddersfield ahead of the final league match of the regulation season.
Mitchell told the Daily Echo: They had a very difficult task and it must have been the hardest job in the world to step aside from the boys and start managing them.
It would have been a recipe for disaster for some people but they have managed it well and have come through. I think they will go on to even better things. They have proved a popular choice and credit must go to them and to the boys for accepting and helping them.
They had a hard act to follow and have followed it fantastically well. They have certainly done their bit.
Everybody should get behind them and the boys during the play-offs.
Whatever happens, we can be proud of ourselves. Our aim at the start of the season was to stay in this division and not return to the league below and we have been successful.
Mitchell, who bought into the club alongside the Murry Group two years ago, added: We have got to focus on building a club which could consolidate in the league above. I think we can do it but it takes time and dedication.
My dream would be to take the club as far as it can go and that would be the Premier League. Blackpool did it and it would not be impossible for us to do it but it would need everybody's effort.
It remains to be seen how far we can go. I would jack in if ever we were to stand still or go backwards.
I am only in it to go forward. When I think my work is done at the club then I will find another challenge.
Football is a business, big business. We have been successful because everybody pulls in the same direction and it is unbelievable how far we have come in two years. It is all down to hard work, not money.
I know some people think we should just throw money at it. But, whether it is us or Barcelona, you won't be successful without hard graft. It has been a team effort from the top to the bottom and that includes our loyal supporters.