The win puts Leinster into the quarter-finals as the second-best runners-up in the competition and they will now face Toulouse in France, while Bath will take on Leicester in the last eight.
O'Driscoll, who celebrated his 27th birthday on Saturday, thought he played only reasonably well just weeks after returning from the shoulder injury he suffered in a spear tackle while captaining the Lions in the first Test match against New Zealand last summer.
He said: "This is my fourth full game back and I struggled in that last 10 minutes. I will be much better for playing in such a high-intensity game and I feel a little closer to where I want to be.
"In parts, it was some of the best rugby we have played this season. I felt a bit disappointed at the end in the way we ran out of gas but if you are playing such a high-octane game, you expect to run out of gas sometime.
"There was huge pressure on our forwards before the game to match Bath's pack and I think they did that with aplomb. Our scrum was excellent and the work rate was good especially in that last 10 minutes when we were under pressure.
"What we were doing was trying to get ourselves into the last eight and our sole goal was to put ourselves into the knock-out stages."
Bath coach Brian Ashton cheekily conceded O'Driscoll was "quite a talented player" and admitted his side paid for their errors.
He said: "If you turn ball over to guys like that, you are on the back foot and we were on the back foot for a long time in the match and put ourselves under pressure.
"We hoped to catch them off-guard but they consistently turned over ball and that's the last thing you do against a Leinster side which has class guys out wide."
Bath hit back from what would have been their heaviest European Cup defeat to within one try of getting a bonus point and, with it, a home draw in the quarter-finals as they scored their second and third touchdowns late in the match.
Ashton added: "At the end of the game, all our players were fully aware of the situation with the fourth try."
Yet the focus was purely on brilliant O'Driscoll after the game, and his head coach Michael Cheika said: "I get the chance of seeing Brian every day and the way he's getting involved now.
"I got the chance to see this week how much he wanted to play well here. I could see the intensity in his eyes.
"And I didn't have to say much to the team at half-time and it was decision time about where we wanted to go as a team in the game, if we wanted to go forward or stall.
"Bath were smart and tried to change the game but we didn't let them play that much. When we took our foot off the pedal in the last few minutes, they did well again."