When someone asks: Do you trust science or some ancient fairy tale.

Not sure what fallacy this is. By using ancient fairy tale instead of the Bible, they create a challenge that isn't the primary challenge. I have to discuss why it isn't an ancient fairy tale before I can discuss the relationship of religion to science. The use of inaccurate term rather than a simple, accurate one.

Do you trust science or some ancient fairy tale.

Basically, this strikes me as a hasty generalization, or some form of ad hominem (Guilt by Association) and possibly Poisoning the Well. You alone would know the context of the argument involved. It sounds like you have good reason to assume they are comparing the Bible to a fairy tale. So that would be the first issue to address without getting into the science v religion debate just yet.

Is the Bible a fairy tale? No, not literally, or structurally. There may be similar elements, and, in fact, the Bible may contain the remnants of early cultural folkloric tales, but in both Jewish and Christian biblical studies many of the stories are considered Midrashim, parables or mnemo-historical accounts. Some believers believe it to be history, others consider The Bible to be mythological. I'm sure most secular scholars would agree that the Bible more closely resembles religious Mythic structure, bios, parables, or historical fiction (Joseph Campbell, John Dominic Crossan respectively).

So, the question deceptively creates a false equivalence between science and fairy tales. One is an epistemological method, the other is a literary genre - two very different fields of study.

As for the science v religion debate, I tend to defer to Joseph Campbell's maxim: There is no conflict between science and religion. There is only the conflict between the science of the 6th Century BCE and the science of the 21st Century.

It depends on what story is being referred to in the Bible. The (protestant) Bible is actually a collection of 66 books spanning many genres. Let's assume one is taking about the creation story. A fairy tale is defined as "a children's story about magical and imaginary beings and lands." From a secular perspective, this is precisely what the creation story is. However, one would expect a fundamentalist Christian who accepts this story as historical fact to argue that this is a false dichotomy , where there is another choice... "God's Word." This will ultimately come down to a debate about belief. If the fundamentalist Christian's belief is true, then we are looking at a false dichotomy , otherwise, we are not. If science is discounted or takes a back seat to the Bible, then there is no common ground to agree if the belief is true or not.