The likely reason is that Bush has made himself quite valuable after racking up 2,072 rushing yards and 588 receiving yards in two seasons with Miami. His versatility and speed — plus him proving that he can handle a regular running back workload, which was always questioned when he was with his first team, the New Orleans Saints — means that other teams are likely to give him a better contract. The Dolphins, meanwhile, are trying to be financially prudent as they rebuild. They also have several big needs to work around, with positions across the offense and defense needing to be filled.
Bush had his career high in rushing attempts this past season at 227, although his yards per carry dipped to 4.3. He also had his second-lowest reception total, but overall, he caught far fewer passes in Miami than with New Orleans, which preferred to use his speed in the passing game.
Bush has proven himself to be a playmaker, but with cheap contracts available for teams signing running backs out of the draft, he could be the latest casualty as Miami tries to get itself into a rebuilding plan that works. The Dolphins went 7-9 last year.