Midfielder Gleeson set the Dons on their way in the fourth minute as they caught Vale cold before Reeves doubled the hosts' advantage moments later.
And Chelsea loanee Bamford had the game wrapped up just after the half-hour with the Valiants creating nothing and the Dons recording back-to-back league wins for the first time this season.
Gleeson opened the Dons' account in the fourth minute with a fine 30-yard effort, his strike flying in off the post to give Vale keeper Sam Johnson no chance.
And then in the 13th minute the Dons doubled their lead when Reeves' shot from the edge of the area got the better of Johnson and found the bottom corner.
Bamford made amend after being denied by Johnson when he met Reeves' low cross for his 15th goal of the season.
Vale boss Micky Adams threw on Chris Shuker and Ben Williamson in the 65th minute to try and spark an unlikely comeback, but it never materialised.