The 19-year-old, who has previously had trials with Brentford and Stoke City, joined central defender Harry Flowers and new goalkeeper Brandon Hall under contract for next season.
Bood, who can play anywhere down the left-hand side, is from Priorslee and a former Thomas Telford School pupil.
He burst on to the scene in the 2021/22 campaign, earning an 18-month contract in January 2022.
And, despite relegation from National League North, Bood will be sticking around for the Bucks' Southern Central Premier campaign.
