As for the recipe sharing: I understand, though I do not share, the possessiveness over personal recipes. But I really can't fathom how, if it is a recipe from a book, one can justify not sharing that. A PP mentions that there is a fair amount of work that goes into finding the worthwhile recipe - that's true, but there's also a fair amount of work (scouring reviews, trial and error) that goes into finding a really excellent restaurant - and I can't imagine refusing to tell a very good friend which restaurants I've discovered, through my own labors of review-scouring and wasted money and Friday nights, are truly worth it all.
As for the email ignoring: there's no excuse for this, assuming the friend actually received the email.
The OP had not ever asked before, and hearing your good friend bean dip a near stranger over the recipe is hardly a sufficient clue that you should never even ask. If the recipe is truly straight out of a book, I can't fathom the friend not sharing it, but even if she didn't, a simple "I'm sorry, but I don't share that" would be light years preferable to silence.
If she has made tweaks, she could say "Well, it came originally from X book, here, but I've made a number of tweaks over the years that I'm not willing to share" or "you know, I've made so many tweaks, that it's really my own recipe now that I'm not comfortable sharing - and the starting recipe is so different, I'm not sure how much help knowing it would actually be."
But just pretending your friend has not spoken? No, there's no good excuse for that. Perhaps she feels bad about the fact that she doesn't want to share the recipe. Too bad - she needs to put on her big girl panties and figure out how to respond like an adult.