The move means that Bore will be eligible to turn out for both clubs as the campaign progresses.
After strengthening his squad in recent weeks, Boston boss Dennis Greene has been forced to ‘balance the books’ which has culminated in Bore’s short-term departure.
Bore’s move to Sir Halley Stewart Field follows Ben Fairclough’s transfer to Grantham Town on a month’s loan.
Greene told bufc.co.uk: “Unfortunately when you bring in two players like Rene (Steer) and Jake (Hall), you have to balance that out.
“We have lost Ben (Fairclough) for a month to Grantham, which allows him to get more games and gets us more in line with the wage bill.
“Peter Bore is a non-contract player. I do not want to let him go, because I want him here, but it might be two or three weeks before I can get him back.”
Reflecting on his policy of keeping his players on their toes, Greene added: “I have always got to tweak things and keep the wage bill in line, so the players know that I will not settle for second best and whether you are on contract or not, if you are not performing to the required standard, I will bring somebody else in and lose a player as a result.”