Manee, your best point is about Shoaib. Bradman himself said of the aboriginal Queensland fast bowler Eddie Gilbert:
The keeper took the ball over his head, and I reckon it was halfway to the boundary, he said, and that the balls from Gilbert were unhesitatingly faster than anything seen from Larwood or anyone else.
Gilbert's pace actually knocked the bat from Bradman's hands (bats in those days were toothpicks compared to now) before dismissing him for a duck. It is arguable that sheer pace was able to unsettle him more than anything, although one must emphasise the importance of rarity to a surprise attack.
Still, the lightweight and arguably dead bats (intended to last much longer than current professional bats), combined with any notion of slower bowling could only have made it more difficult to score at the rate that he did (determined to be around 60 runs per 100 balls by Wisden statisticians).
I think the strongest argument that Bradman would have prevailed in a modern game is his contemporaries. One would think, if conditions were brilliant for batsmen, then there would be more with averages over 60 or over 80. Of course, there aren't. There were definitely great batsmen, though. England's Wally Hammond was an undoubtable dominator. Hammond is to this day the third best scorer of double hundreds and yet his career average was a mere 58.
Of course, there is no way to judge how these players would have worked in a professional era. Still, the ridiculous difference between Bradman and his contemporaries and the continuing ability of some rare batsmen to average close to or over 60 suggests to me that sheer ability could count for an awful lot, whatever the conditions.