Let's check out Batman #57:
Hmmmm... that kind of behavior might have been the norm in 1950, but I think that Bats would be asking for trouble these days. Instead of just grabbing her, there would have to be a clear understanding along the following lines:
Batman: Excuse me, Miss?
Hiker: Oh, thank Heavens you're here, Batman!
Batman: Yes, I saw that you seemed to be having some trouble. Not that I'm implying you need my help, or that of any man.
Hiker: No, it's fine! Please help!
Batman: Are you certain? I don't want you to feel devalued or compromised as an individual. The last thing I intend to do is to rob you of the self-esteem that can only come from hoisting yourself to safety.
Hiker: Please help! My hands are getting numb!
Batman: We don't to compromise the long term issue (ie, your feelings of independence and self-worth) for the short term (ie, you falling to your death). While I acknowledge the strength and bravery inherent in the very act of asking for help, I don't want you to fall prey to society's notion that, as a woman, you require a man's help to... for lack of a better term... "rescue" you.
Hiker: PLEASE DO SOMETHING!
Batman: And, of course, there is the rather awkward reality that some sort of physical contact is all but required in this sort of situation. I want to make it perfectly clear that I would be using only the physical means necessary to effectuate your rescue. I can assure you, Miss, that I would not be receiving any sexual gratification from the aforementioned contact. I would further offer that, although you are wearing shorts and a rather form-fitting top, I respect your choice to dress how you choose and acknowledge that, regardless of your clothing selections, you have every right to expect respect and...
Hiker: AIIIIEEEEEEE!!!!!!!! (Splat!)
Coming this month: Batman. Only on the Lifetime Network.
Yeah, that was silly. But how much are you paying me?
The first story in this 52 page for a dime extravaganza was a trial wherein the court examined the fitness of Bruce Wayne to continue as Guardian for Dick Grayson. Not that they know the half of the child-endangerment situations Bruce Wayne put that kid in.
And do you meet anonymous strangers in the dead of night often, Mr. Wayne?
You'd be surprised.
What? Objection, Your Honor, to counsel's snide editorializing of Mr. Wayne's testimony!
Geez, I guess billionaire Bruce Wayne can't afford aggressive legal representation.
Yes, it's very sad, Dick.
But, Bruce! You could adopt me! That way, a Guardianship (which is temporary by design) would be moot! We would have the same rights to each other as we would as if you were my biological father.
Yes, it's very sad, Dick. If only there was something we could do.
Bruce? Didn't you hear what I just said?
Very sad, Dick. Very sad.
I guess I'm just in a silly mood today. The changing of the seasons does that to me.
Hey! It's time for Fun with Out of Context Dialogue! (tm!):
That's what SHE said!
Yeah, I know. You're wondering why you kept scrolling down today. I have no good answers for you.
Uh-huh. And not five pages earlier:
Did you notice that in the flashback, Bruce and Dick are eating roast again? Those guys must really like roast. If they aren't having breakfast, you'll almost always see them eating roasts. Don't make me prove it.
Anyway, security at Stately Wayne Manor clearly ain't much. Even though no one knows he's Batman, there's always that whole "billionaire" thing that may necessitate a few measures that might discourage people from peering at you through your dining room window. And you certainly wouldn't want to just drape things like Batman cowls in a chair like that.
Then again, I'm not a rich guy, so what do I know? Maybe that's just how rich folks do.