from the Real World
There have been many screen adaptations of Robin Hood, but it is difficult to determine which one it was. It may have not been any Robin Hood film that existed in the real world. The Park Row tragedy that happened shortly after their viewing of the film would have had to have happened sometime between 1948-1950, this is assuming Bruce was eight years old, ten at the most. In most versions he's said to be eight.
Still, in the real world, no such Robin Hood film came out between those years. Ten years earlier The Adventures of Robin Hood came out, and it was likely replayed in many theaters over the years, and probably still played frequently ten years afterward, so it's not a stretch to imagine that it was the 1938 version. But this is all just conjecture.