The pair, who have made 16 Robins appearances between them so far this season, have headed out to Plymouth and Forest Green respectively.
Bryan, 19, and Burns, 17, have featured in both matches for their new clubs since making the loan moves, with the latter opening his goalscoring account for the club on his full debut in the Blue Square Bet Premier.
And O'Driscoll admitted he was not concerned about which league they were playing in, just that they will play enough matches in the coming weeks.
O'Driscoll said: "We had to look at the bigger picture.
"If they are going to be massive parts of this squad next season then the more football experience they can get actually playing games the better.
"Both are good clubs and I've kept them and kept them because if I have a problem I could stick them on the bench but they need to go and play games.
"Both clubs have indicated they will play both boys which is fantastic for Wes who is going to play up front, and Joe is going to play in midfield."
The City head coach also confirmed that fellow youngster Bobby Reid, 20, is still with the npower Championship strugglers but he would not be against a similar loan move for the midfielder.