Doyle had already found the net from close range to put Wanderers 2-0 up at Ashton Gate when he picked up the ball just outside his own penalty area.
The Republic of Ireland international striker embarked on a lengthy counter which took him past two City defenders and all the way into the Robins penalty area, where he finished low across goalkeeper Tom Heaton.
And Doyle has revealed the part boss Solbakken played in his thinking.
"I was pleased with my second goal," he told Wolves' official website.
"The manager has been on at me a fair bit to run more with the ball and take people on more, and maybe that was in my head.
"Sylv (Ebanks-Blake) made a good run and took one or two defenders away and it opened up for me."