two ways to approach this, depending on which direction Bob takes the argument.
1) Alice seems to be accepting Bob's implication that probability exists in reality, rather than only in the minds and models we use to predict it
A fair bit of recent discussion can be found in this thread, and in the sequences in Probability is in the Mind.
I'd summarize as "the probability of something that happened is 1". There's no variance in whether or not it will occur. If you like, you can add uncertainty about whether you know it happened, but a lot of things approach 1 pretty quickly.
The probability of future experiences will be 1 or 0 at some point, but for now, different agents assign likelihoods based on their priors. The probably that the next sequence of flips will be exactly this is, in the world, 0 or 1 - what will be will be. The probability that an agent can use to predict this experience is 1/2^n. That probability expectation changes as evidence is added, such as the evidence of seeing some or all of the flips.
alternate way of showing this: ask Bob to show his update after each of the N flips. The prior is indeed 1/2^n, but each observation makes it twice as likely.
2) Bob's just wrong if his priors give a significantly higher chance to supernatural physics violations than to winning the lottery. This is probably some form of scope insensitivity. For both ghosts and lottery-winning, I do assign a much higher chance that I'm being tricked than that it actually happened, but if the question comes up, I can gather evidence to change those ratios.
Alice: "I just flipped a coin [large number] times. Here's the sequence I got:
(Alice presents her sequence.)
Bob: No, you didn't. The probability of having gotten that particular sequence is 1/2^[large number]. Which is basically impossible. I don't believe you.
Alice: But I had to get some sequence or other. You'd make the same claim regardless of what sequence I showed you.
Bob: True. But am I really supposed to believe you that a 1/2^[large number] event happened, just because you tell me it did, or because you showed me a video of it happening, or even if I watched it happen with my own eyes? My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?
Alice: Someone usually wins the lottery. Should the person who finds out that their ticket had the winning numbers believe the opposite, because winning is so improbable?
Bob: What's the difference between finding out you've won the lottery and finding out that your neighbor is a 500 year old vampire, or that your house is haunted by real ghosts? All of these events are extremely improbable given what we know of the world.
Alice: There's improbable, and then there's impossible. 500 year old vampires and ghosts don't exist.
Bob: As far as you know. And I bet more people claim to have seen ghosts than have won more than 100 million dollars in the lottery.
Alice: I still think there's something wrong with your reasoning here.