Ex-Leeds prop Bailey, 31, joined after the start of the season and made 15 appearances for Wire.
Forward Cox, 24, arrived on a one-year deal from Hull KR while Australian prop Dodds, 27, had an injury-hit season.
"I'd like to thank all three players for their contributions over the season," said head coach Tony Smith.
Super League side Warrington Wolves have announced Ryan Bailey, Jordan Cox and Mitchell Dodds will leave at the end of their contracts.