Three years is a long time of doing absolutely nothing (other than archery of cawse). It certainly was enough time for people to make up urban legends about him . . . like Batman.
I doubt he did anything important in the other 5 considering the plot doesn't tell us he accomplished anything noteworthy. How do we know he was still Playboy Bruce? We don't. All we know is he tried to pull a Tony Stark (which is odd considering clean energy was never of interest to Wayne Enterprises or Bruce Wayne in general) and failed miserably.
OP makes a good point, misunderstanding of the whacked out time frame or not. It's not just the time frame that should tip people off, it's how close Bruce Wayne and Batman come back into the world. The same issue happened in Batman Begins. The guy is gone for 7 years, comes back and makes the papers. People thought he had been dead for years (just like people in TDKR thought he was pissing in jars or horribly scarred), he comes back, then this Batman fellow shows up. Then again, I still fail to realize how ordering a batch order of 10,000 cowls and 10,000 pairs of cowl ears avoids suspicion. How is ordering one or two more
suspicious than ordering a frivolous amount. Bruce Wayne ordered 10,000 cowls and ears after he's been dead for 7 years? This Batman guy who's clearly dressed up in costume shows up? WHAT!?!
Not very subtle. The only smart one in the city was Coleman Reese. I guess I should include John Blake in there, but he never deducted it from any of the information discussed in this thread. He deduced the secret from . . . a feeling of anger in his bones, facades and DEM BONES.
The dumbest one was Selina Kyle, who interacted with Bruce the hermit, Bruce the grinning billionaire, and Bruce the Batman and never put three and three together until Bane called him mister Wayne. This was even after Bruce actually pulled the old "Batman's my bro and a mutual friend" speech!
I couldn't believe Nolan and Co. played that card. It was straight from the Mask with Jim Carrey.