For 20 minutes, it appeared the 29-year-old's header would cause the shock of the tournament so far.
Edin Dzeko eventually levelled for a laboured City outfit, who now face a replay at Eastlands before they can claim a fifth-round clash with Aston Villa.
It provides another lucrative fixture for County, who will travel to the north-west in confident mood, having already dumped Sunderland out on their own patch in the previous round.
And for Bishop, it provides the opportunity to create even more happy memories in a professional career that did not begin until he has 25.
"It took me a while to get my chance in the Football League but I was always confident once I got there I could do myself justice," said Bishop, who had spells at Whitby and Scarborough in the lower reaches of the non-league before moving to York and then Barnet.
"Scoring this goal is the best moment in my career.
"Now we have a replay, which I want to enjoy because I may never get the chance to play at a stadium like that again.
"But it is also a game of football. It doesn't matter whether it is the Sunday League or the FA Cup, you want to win."
The most pleasing aspect of yesterday's game from Bishop's perspective was the manner in which County went about their task.
They may have been helped by an abysmal pitch, churned up by the two rugby matches that had been played on it the previous week, but at no stage were the hosts overrun by a side not that far away from Mancini's first-choice XI.
"I heard a few comments after the Southampton game against Manchester United on Saturday with people saying teams like that tend to tire after an hour," he recalled.
"We didn't do that.
"Even after City equalised I thought we had the best two chances.
"It says a lot for the backroom staff that they have got us so well drilled and got our levels of fitness so high we can compete with this lot for the full 90 minutes."
Any side coached by Paul Ince is unlikely to be lacking in motivation.
And Bishop acknowledges the Sunderland triumph this season, and a defeat of Wigan in last term's run to the fifth round, means there will be no sense of inferiority from the Magpies when they head to Eastlands.
"There is history there," he said.
"It can be done. What we are hoping for is not an impossible thing.
"You try not to be in awe of them and start thinking about what their team is worth.
"We had earned the right to be on the same pitch as them.
"As the manager said, we showed them respect until one minute before kick-off. After that there was none."