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So why does the reciver need the two bits?

I'm not prone to study too deeply because I've learned (apparently) very bad analogies or schemes for entanglement.

The teleportation process involves using a measurement to entangle the receiver's side of the pair with the original state in a useful way. Since measurements are probabilistic (and the measurement is along two qubits) there are four outcomes of this measurement with four different kinds of "garbling" of the transmission (one of which is no garbling).

The receiver needs the two bits to choose which of four kinds of garbling occurred, so it can correct them with the appropriate post-processing (if necessary).

So it's kind of like a traditional error-correcting code, just sent along a separate channel?

Sort of. The only issue with that interpretation is that either piece of data in isolation conveys none of the original information, even probabilistically. A better analogy would be sending two classical bits by different channels, with the desired bit being the XOR of the two, and one of the bits being chosen by a random number generator.

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