I really don't see much influence from the Bronze Age Bats in Nolan's Batman. A lot of the plots from various post-Crisis stories are used across the three movies but this Batman was something new. Nolan deliberately set out to create a relatable human being the audience could empathise with. He was pretty much a normal guy with normal dreams and desires. He didn't have the hard edge, obsessive drive and polymathic attributes of any of the comics interpretations or the willingness to surrender his entire life to crime-fighting.
The Golden Age Batman was a mysterious, silent vigilante who was primarily interested in terrorising the underworld and didn't particularly mind if he killed a few along the way. That to me was Burton's Batman.