What sets Bradman apart from your average batsman is his ability to regularly convert 100s into 'mega-centuries'. While the ability to do this would be highly desirable to every cricketer only a handful of batsman are able to score 'mega-centuries' because the strain on the necessary levels of concentration is enormous. Importantly, I don't think that raw batting talent alone (ie. 'hand-to-eye coordination) has much to do with achieving a very high batting average. A moderate average yes, a very high batting average no. One only has to consider Mark Waugh or David Gower to grasp that fact.
Therefore, the question is - what would stop Lara or Sangakkara (for example) averaging 90+ during the 1930s should a miracle happen and they be transported back in time to Bradman's era at peak form? I can't think of any impediment because they have abundant raw batting talent, the proven ability to concentrate for long periods of time, and the relatively unique experience of playing cricket during the 90s-00s which would be invaluable. You would merely give them their brief and tell them to get on with it - 50 odd Test matches spread over a dozen playing years, no ODIs, flat tracks, and minimal numbers of express pace bowlers. The conditions couldn't be better for batting apart from the want of a helmet.