The former Middlesbrough defender was laid low by a stomach bug just after Derek McInnes' dismissal, and has yet to feature for O'Driscoll.
City are at the foot of the Championship despite some encouraging results since O'Driscoll took over, which happened when Bates was on the cusp of signing a new contract at Ashton Gate following a run in the side under McInnes.
"It was a difficult situation when the manager went. I'd spoken to him on the Saturday and arranged to come in on the Monday morning and sign a contract," Bates told the Bristol Evening Post.
"By the time I got home that evening, Derek had lost his job and everything had changed.
"I spoke to Sean O'Driscoll a few days later and he told me he would have to look at me in training before making a decision. It was a difficult situation for both of us, but I understood where he was coming from.
"The same day I spoke to the new gaffer, I also went down with gastroenteritis and ended up being bed-ridden for two weeks.
"The timing of the whole thing could have been better. But that is how football works and you just have to get your head up and work hard."
Having recovered from his illness, Bates has made it onto the bench in recent weeks and is beginning to see a brighter future for himself.
"Fortunately, the gaffer was prepared to wait for me and, once I got back fit, he must have seen something in me, because he offered me a contract," added Bates, 26.
"I've been training for four or five weeks now and I'm enjoying being a part of the new regime. Sean O'Driscoll has not spoken to me about my situation long-term, because he is a team manager and speaks to the team rather than to individuals.
"Everything he does is about the team and being organised as a group. It is credit to him that it is working, but also credit to the players."