Why Didn't they stop Bourne at the Bank?

I have a feeling that the source at the bank simply had standing instructions to inform Treadstone whenever Bourne visited up at the bank. He probably wasn't aware of the fact that Bourne's mission had failed, or that he had supposedly turned rogue.

Given the highly sensitive nature of Treadstone, its highly unlikely that anyone other than Conklin and his team back at Langley knew everything that was going on.

Well at the point in the movie they have no idea what is going on. So right now it's simply track and observe.

When the bank agent behind the bars makes his phone call, he can't know yet what Bourne took out of the deposit box. In fact, he can't know yet that Bourne took anything out of the deposit box.

Also, we don't know that the bank agent even knows it's Jason Bourne. In fact, the bank account could be in one of the other identities and not Jason Bourne at all. The bank customer is identified by biometrics, not name. That would be appropriate given the bank secrecy associated with a numbered account.

Presumably, the bank agent was given some sort of instructions that prompted him to call someone, but we don't know what he was instructed to do and we don't know who "someone" is. Eventually Bourne is identified and the deposit box is examined because after the Zurich consulate fracas, Conklin says to Zorn: "I liked it better when I thought he was dead". Conklin had just arrived at Langley and he & Zorn were taking the elevator up to his office. Given the time difference between Switzerland and Virginia, it must have been early morning at CIA HQ. Given that it was morning in Zurich when the consulate fracas occurred, I'd say that it took half a day for the word to get from the bank to CIA HQ.

Given all this, do you still ask why Bourne wasn't stopped at the bank?
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