Steve McClaren, who endured an ill-fated spell in charge of England, was appointed as Nigel Clough's successor at Pride Park on Monday evening. He did not officially take charge of Tuesday evening's incredible match with Ipswich, but did enter the dressing room at half-time to deliver a team-talk which has been credited with Derby coming back from 4-1 down to draw 4-4.
Bryson led the charge, scoring a second-half double, including the 88th-minute equaliser.
Now the former Clyde and Kilmarnock player is looking forward to working under - and learning from - the respected coach.
"He [McClaren] has got a great cv, he has managed England and has shown great potential," said Bryson. "With Steve coming in, we need to give him our full support. Whatever ideas he brings to the table we need to take them on and use them in matches.
"I am sure that he will be delighted with what he has seen in the second half from us, but I doubt he will stand for that sort of performance in the first-half. We need to put it right on Saturday."
Bryson was handed the captain's armband for the first time in his Derby career in midweek with the regular captain Shaun Barker injured and Richard Keogh suspended.
He expressed his pride at leading the Championship outfit against Ipswich, especially when his own contribution on the night proved so significant.
"It is a real honour for me to be captain at such a big club," said the Scot. "Even though it was just for one night because Richard was suspended, it is still a great achievement in my career."