I really would not recommend trying to sneak bleach through. That is not one of those "only the US bans it because they are wackos" type of items. Most airlines worldwide do not allow corrosive and/or oxidizing chemicals on board their planes in luggage. I am not sure exactly the reasoning, but it seems serious enough that it is just universally banned.
Even if you say you didn't know any better, the TSA CAN give you a REALLY hard time if they find something prohibited in your luggage. Yes, they ordinarily take it and leave you a note telling you not to bring that anymore. But they can pull you off the flight and make your day very unpleasant. Some of them are pretty cranky sometimes.
I just would not take the risk of getting that one over cranky TSO. I would hate to hear about a ruined vacation because of something like that.
And I agree, it bites about the Tide pens...I thought they would be a great alternative to the bleach pen. I have 2 little ones and really like to treat stains. We have an Owner's Locker down there since we go so often and I bought Zout down there and leave it.