You don't have to be a 'Bradman fanatic' to think he would have averaged the same. A lot of time people bring out the argument that the game's changed a lot since Bradman's time, and yes, it definitely has. However, I'm still confident that he'd perform the same way, assuming he was playing today.
For every argument that bowlers are faster, reverse swing is around, etc., there's the argument that batsmen now have more protection and bigger bats. That is, while bowling has come along a lot since then, so too has batting. If Bradman were to be playing today, there's no logical reason to believe that he wouldn't benefit from these advances in batting any more than the bowlers would benefit from the advances in their respective fields.
I'm pretty confident this is the case, because since Bradman's time, the balance between bat and ball has remained relatively the same; the good bowlers still average under 30 and the great ones under 25; the good batsmen still average over 40 and the great ones over 50. Yet Bradman still stands out as an anomaly, both in terms of Test cricket and FC cricket. No one's come even close to him yet.
So for mine, the argument that fielding standards have improved so much over time, or bowlers have becoming better, doesn't wash for me. If you were to jump in a time machine, go back to the 1930s, bring Bradman up and throw him in against South Africa tomorrow, then yes, I'm pretty certain he would struggle a bit. But if were born, raised and trained in today's environment, there's absolutely no reason IMO why he wouldn't be as successful, if not more. Assuming the coaches let him get away with his unorthodox batting technique, that is.