Bush made four catches for 42 yards and carried the ball 19 times for 65 yards for the Dolphins (7-8), whose slim playoff hopes were dashed when Cincinnati bested Pittsburgh earlier Sunday.
Ryan Tannehill completed 13-of-25 passes for 130 yards with two TDs and no interception for the Dolphins.
Lamar Miller led Miami's rushing corps with 73 yards on 10 carries.
Ryan Fitzpatrick picked up 240 passing yards on 20-of-35 efficiency with a touchdown and an interception for the Bills (5-10).
C.J. Spiller rambled for 138 yards on 22 carries in Buffalo's loss.
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