The Teessiders head for Ashton Gate desperate to avenge their 2-1 home defeat by City on October 30 last year to ease themselves further clear of the npower Championship drop zone.
Mowbray said: "It's a game that's winnable but also we understand it is a very tough fixture.
"The actually beat us in that first game. It was a game where, for spells, we were right on top and in other spells we weren't very good.
"I think we have become more consistent since then and I would hope we would go down there and find a good consistent performance and get a result.
"It is just the next game and a chance for three points."