White took 3-5 from just 10 balls in Saturday's first one-day international against Bangladesh but said he wants a longer bowling spell in the second game.
"It's nice to get a few wickets, but it would have been nice to get a few more overs under the belt as well," the legspinner said.
"Hopefully from this game (on Wednesday) I can get more of a bowl."
White has never bowled more than six overs in any of the 19 one-day games he has played but a chance for a bigger role in the bowling line-up beckons after Brad Hogg's retirement and the dumping of allrounder Andrew Symonds from the team.
The 25-year-old, who is a middle-order batsman, said it was also hard to judge whether his bowling was improving, given his lack of overs.
He said while he was happy with his performance in the practice nets, "under the pressures of a game is where it counts to me the most, and that's what I've got to prove to myself and my teammates and the opposition -- that I can do it at that level."
Australia play their second one-dayer against Bangladesh in the northern city of Darwin on Wednesday.
Allrounder Shane Watson is expected to play after he trained at full pace Monday after missing the first match due to soreness in his calf and in the toe he broke in the Caribbean.
Watson is likely to replace James Hopes or paceman Brett Geeves.
Bangladesh, who lost to Australia by 180 runs on Saturday, will be without batsman Roqibal Hassan, who sustained a broken thumb from a Geeves delivery in the first game.