Drury told the club's website: "Bartle came to the decision that he just couldn't leave the club he loves. He's enjoyed every minute of his time here and when offers from other teams come in, he just tells them straight away, he's signing for Stamford.
"Connor has been brilliant for us since day one, he's a leader and has an unbelievable left foot. His assists are high and he enjoys setting goals up for his teammates. He can also chip in with a goal or two. I'm so chuffed with the way he conducts himself on and off the pitch, I feel this is another top signing for us.
"Joe Burgess has played centre midfield most of his time for us, I feel he's one hell of a full-back with his energy to get forward and his ability to cross a ball. He will be another key member of this squad going into 2021/22.
"Joe, like a few of our lads, turned down a silly offer from a club at this level and a decent offer from a level above. Joe also has an eye for goals and has been our top scorer before. I believe having him as our full-back will add plenty to the team.
"Once again unbelievable commitment from another top lad and top player. I honestly can't thank my players enough for sticking with the team and to be playing for me again this season."