Walton, 19, made four appearances for the Championship club last season, keeping two clean sheets.
"He has superb agility and mobility and is extremely comfortable in possession of the ball," Bury manager David Flitcroft told the club's website.
"Christian shows a great desire to keep the ball out of the net and maintains a strong presence within his area."
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League One side Bury have signed goalkeeper Christian Walton on a season-long loan from Brighton.