The talented defender has been a mainstay of the Brig first team squad for the last two seasons and was an ever-present during the 2022/23 campaign as the club made it all the way to the Northern Premier League play-off final.
Skinner will now link up with a Hereford side that finished 16th in the National League North last season.
A Bamber Bridge statement read: "Although we are naturally gutted, we are always incredibly pleased for Aaron for getting the opportunity and he massively deserves it.
"We all wish Aaron all the best in his move and next stage of his career. He’ll always be welcome back at the Irongate."
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