Ludlam and Lawes were back from England duty and the duo spearheaded Saints' charge towards a crucial Gallagher Premiership bonus-point win at Ashton Gate.
Both players delivered tireless displays as the black, green and gold overpowered their hosts with a dominant display.
Talking about the showing of skipper Ludlam, forwards coach Dowson said: "That (performance) and the way he's led the week has been outstanding.
"He came back in from England camp, which can be tough, and he was disappointed not to have played but the way he's led this week has been brilliant.
"He's brought energy throughout the week and he's made sure everyone was pulling in the right direction, getting people back into the group who have been on international duty.
"He's a fantastic leader and he carried that right the way through the game as well.
"I loved watching him this week.
"He gets that experience and he has lots of people who have experience around him and can point him in the right direction, but he's really relishing that role.
"He's a bright lad and he picks things up very quickly."
Lawes captained England twice during the autumn, earning wins in both matches.
And he showed his class for his club against Bristol.
"He's unbelievable," Dowson said.
"He's brilliant, he was one of the best, if not the best player, on the Lions tour.
"He was fantastic in the England camp.
"Is there anything he can't do?"