Anderson links up with the Bucks after having his contract with Northern Premier League side Lancaster City terminated by mutual consent earlier this week.
This season, he had made seven appearances for the Dolly Blues.
In 2017, Anderson was part of the England squad that claimed U17s World Cup glory in front of over 66,000 fans in Kolkata, India.
Now he will join a Bootle side looking to steer further clear of the Pitching In NPL West Division relegation zone, starting on Saturday away at struggling Hanley Town.
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