Charles Davis (who's probably as reliable as anyone for this) has Bradman's run rate at 61-62, and Hammond's as 45-46. (The other notable #3 of the era, Headley, was about on a par with Hammond at 44.1)Considering he was striking twice as fast as Hammond (if I'm not wrong).. he would be absolutely gun in LOIs. He'd just bat the entire 20 overs most of the time.
The fastest batsman of that era was Maurice Tate (75-76), who was of course a bowling all-rounder. McCabe and Gregory scored at about Bradman's pace, with Woolley (who was an earlier era but overlapped with them) just behind them. Of pre WW1 batsmen, Trumper and Sinclair were faster.