What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

I don't know if there are any particular topics you're interested in, or at what level of detail you want them presented, but Knuth's Surreal Numbers is an example of the sort of book you mean:

B. You mean we're actually using the New Math to decipher this old stone tablet?

A. I hate to admit it, but that's what it looks like. Here the first rule says that every number $x$ is a pair of sets called the left set $x_L$ and the right set $x_R$: $$x=\langle x_L,x_R\rangle.$$

B. Hold it, your notation mixes me up. I don't know what's a set and what's a number.

The Number Devil: A Mathematical Adventure Is very good; It explains complex concepts in ways simple enough that young children can understand them, yet complex enough to maintain an adults attention with the revelations and connections it provides.

I don't know if it counts as a math book, but Hofstadter's "Gödel, Escher, Bach" contains a large number of very entertaining dialogues that help to explain concepts in logic such as Gödel's incompleteness theorems, usually disguised in the form of some kind of fable involving Achilles and the tortoise.