The Isle of Wight born midfielder had just come back of his holidays and decided to stay with the Cherries as they look to get back into League One after they where relegated last season.
Copper has signed a two-year-deal with the Dean Court club which was similar to the one the Railwaymen had offered.
This is the latest setback for Steve Holland as he looks to strengthen a poor Crewe side that narrowly avoided relegation last season.
Holland has already had rejections from Anthony Elding, Steve Morison, Greg Fleming and Steve Mildenhall over the last few weeks.