The Blades have enjoyed a fine start to the season and remain unbeaten in League One in their opening 15 games, winning four of the last five by a 1-0 scoreline.
In contrast, Rovers are struggling in League Two and United travel to the Memorial Stadium as firm favourites to advance to the second round.
But Collins remains wary and said: "It will be tough at Bristol. They will be really up for it so we need to be as well.
"It is important from our confidence point of view to go there and put in a good performance and try to keep our unbeaten run going.
"Whenever you cross that white line as a professional footballer you want to win and Saturday will be no different."