According to the story she chose after each cup, not at the end (so it's harder for her to make use of the 4-4 information); therefore, the odds calculation is not so straightforward right?

I was thinking the same thing! I think those would be her odds if she were permitted to go back and change her mind about which cups of tea had milk first. If she said the first 4 cups were milk first with some confidence, but on the fifth cup was absolutely certain it was milk first, she would have to go back and change a previous evaluation (because she knows there can be only 4). But because they were presented one at a time, and Bristol made her determination up front. It's basically a series of independent Bernoulli trials (i.e. Binomial distribution). So, assuming she had a 50% chance of guessing correctly, the probability would be (8 choose 4) * (1/2)^8.