After the argument, when Crowley kisses Aziraphale, he tastes something strange - almonds. Suspecting there was chicanery with Aziraphale's coffee, he stops time, Aziraphale clears his system, and they talk quickly - but for the sake of the earth they have to separate. Now it's a race with time to find the Son of God and stop the Second Coming.
And as soon as they're done with that, they're going to have a very long conversation.
When Aziraphale goes to donate a misprinted Bible for a charity auction, he somehow accidentally ends up auctioning himself. He's horrified to be won by a 'lanky man in black', and determined to tell the man that there's been a mistake when they meet after the auction to discuss the date. There is no way he will be going out with some complete stranger that 'bought' him.
And then he actually meets the lanky man in black, and starts to think that perhaps going on the date might not be such a bad thing.