Crisis and Miller. The answer is always Crisis and Miller, with Batman.
Post-ICk some of Bruce's pre-Crisis, um, sanity, seems to have been restored to his history, and it looks like the old guard JLA all knew who he was again, but there was a long stretch there where the whole Antisocial Urban Legend thing meant nobody outside the Batclan, Clark and Diana knew who was under the cowl until the JLA "Divided we Fall" trade, unless (like Dinah here) they quietly figured it out and kept mum.