Burns scored 20 points, including a delightfully-worked try after just 39 seconds, and he is in pole position to start England's Tests against Argentina in the absence of Owen Farrell and Toby Flood.
"Everyone is aiming for the same goal which is four wins out of four and that added responsibility is something I try and thrive on," Burns said. "Hopefully I can keep growing and guide the team through a tough tour. I have a say in the way I want the game played and against the Barbarians we did try and get the ball to wider channels and the boys were devastating out there."
He added: "I was happy with my game management. We kicked when we should and we played when we should. There were lots of pleasing signs moving forward."
England scored five tries in total against the Barbarians, with wing-men Christian Wade and Marland Yarde, Kyle Eastmond and Billy Twelvetrees joining Burns on the score sheet.
Yarde enjoyed an eye-catching senior England debut, scoring one and sending Burns over for his try, to enhance his hopes of starting the first Test against Argentina on June 8 in Salta.
"I am very fortunate at Gloucester to play with young quick backs - and to come here they are even quicker," Burns said.
"You have to give the ball to them and let them do what they do. we all saw how dangerous they can be."
England's first tour match is against a South American XV in Montevideo next Sunday, when head coach Stuart Lancaster is likely to give Stephen Myler the fly-half role.
Lancaster is anxious give a number of England's Northampton contingent the chance to play that first game to help them move on from Saturday's Aviva Premiership final defeat to Leicester.