Warning: this comment contains a rant
"You're on probation, and as long as that's in effect, you don't learn any of the big secrets." Check RED FLAG! "And the first time you disobey my orders--even in a minor way--is the precise moment you're out. No second chances." Double check BIG HUGE FUCKING RED FLAG!
Ohhhhhh the manipulative horribleness. Taking on a real partner-apprentice in crime-fighting, the way a Robin is expected to be to Batman, should never, ever, be a light matter. It's so fucked-up and wrong that Batman would be willing to jerk her around like this, and give her such unreasonable standards to which he never would've held Dick or Tim, or even Jason.
This isn't just an injustice to Steph, it's an injustice to Bruce's character as well. Because no way is he dense enough to not realize that taking on someone as Robin, even she's a she, is going to going to put the two of them in an intense, if sometimes emotionally subdued, interdependent working relationship. The amount trust that can be abused here is huge, but the lack of trust this Batman shows Stephanie is what really makes me sick.
He didn't trust her enough to tell her about Matches Malone (and that lack of information is what made the War Games gang war doomed to failure from the start), which means he didn't trust her enough to really be Robin. Which means he was, as you say, setting her up for failure from the start. Which makes Batman a horrible, horrible person. And while Batman may be emotionally fucked up in many, many ways, my Batman is not that horrible.
Also, the "we may have to do something with your hair" comes off as kinda creepy. What? A pony-tail's too practical? Oh, no, wait, I get it. Alfred just cut him off before he was able to finish: "And we may have something to do about your hair. Here's some black hair dye."
If only she'd kept up the black-haired/blue-eyed tradition, Batman would've treated her right!