All three players joined Warrington in pre-season of 2016.
Bailey, 31, made his club debut in May of this year. He went on to make 15 appearances in the primrose and blue making an impact off the bench including two on the big stage; the Ladbrokes Challenge Cup Final at Wembley and First Utility Super League Grand Final at Old Trafford.
Cox, 24, kicked off his Warrington career at the start of the season in February, making 18 appearances in total.
Blighted by injury Dodds, 27, made just two appearances for the Wire in the one-point nail-biter away to Salford and the away fixture against Catalans the following week.
Head of coaching and rugby Tony Smith said: “I’d like to thank all three players for their contributions over the course of the season.
“They all played their part in helping us achieve the League Leaders’ Shield and making it to two finals. I wish them all the very best for the future and good luck in the next chapter of their careers.”