The 52-year-old former Doncaster and Nottingham Forest boss was unveiled at Ashton Gate on Monday morning, after the club parted company with manager Derek McInnes on Saturday following the 4-0 defeat to Leicester.
O'Driscoll, who had spent the afternoon watching a Blue Square Premier match, was contacted late on Saturday night and travelled to the south west on Sunday for an in-depth meeting with the City hierarchy.
Having signed a 12-month rolling contract the Irishman will now meet his players for the first time on Tuesday and will have just five days to prepare for the trip to Leeds, the beaten opponents in the final match of O'Driscoll's reign at Nottingham Forest.
And with his new employers six points from safety and with just six wins under their belt all season he knows they need to start chalking up victories.
"We have got to hit the ground running, I haven't got time to assess the squad," he said.
"I know most of the players from playing against them or seeing them play so I have an opinion of the players as they will have an opinion of me. But what is most important in football is the character of the team and I don't know that. I have got to create a little bit of trust quickly.
"My message to the players will be 'show me what you can do.' That doesn't always mean how many goals, how many times you can keep the ball up or how clever you can be. It is more the attitude you show when things don't go your way.
"This is a great opportunity for the players to show me when it hasn't gone their way that they are up for the fight. We've got to do it together."
McInnes' assistant Tony Docherty also departed the club at the weekend and O'Driscoll spoke to the gathered media about his desire to get a second of command sorted in the near future.
"It is something we need to address pretty quickly," he said. "The board have people in mind that they think might be a good fit for Bristol City. There are also people I know and people who I haven't worked with who have been recommended to me. So there are three avenues to go down.
"There are various people that have expressed a desire to join the football club and if I can do it quickly then I will."
O'Driscoll inherits a side who are 24th in the division, have not kept a clean sheet since April and have a goal difference of minus 16 but despite their precarious position, he believes they are capable of escaping danger.
"I think the squad of players is, with one or two additions, as good as anything in the division," he said.
"I think there is a feeling within the people that I have met that staying in the division is a distinct possibility. No-one is resigned to anything."