The 25-year-old, who is capable of playing at right-back, on the right wing or up front, will be best remembered by United fans following his exploits for Grimsby Town against the Pilgrims in 2006-2007.
Bore struck twice from the bench as the Mariners overturned a two-goal deficit against the Pilgrims to win 3-2 at Blundell Park in August 2006, before bagging a hat-trick during Town’s 6-0 win at York Street in February 2007.
Bore has since played for York City (on loan), Harrogate Town and Lincoln City — prior to his 10-game spell with Gateshead at the end of last season.
United boss Dennis Greene, who is continuing his search for defensive reinforcements, told bufc.co.uk: "Peter is a great signing for us. He is equally adept at playing in two or three positions and will add real versatility to our squad — not to mention undoubted ability."
Bore is the fifth signing of the summer following the earlier arrivals of Ashley Timms, Carl Piergianni, Gary Mills and Ricky Miller.