The thing is, anywhere is fine to ask a woman for a date, and nearly any time, too. With this caveat: You have to do the groundwork first. You have to meet her in some way, let her get to know you and trust you; you need to know that she’s available and amenable to dating in the first place. You have to be a somewhat known quantity in her space – unless she’s a professional working girl and all you’re doing is agreeing on a set price for services that we won’t mention here.
The tongue in cheek idea that I first mentioned may be a decent way to break the ice and meet someone in an offbeat way that helps to lower her guard to allow you into her space to make that first impression, the first introduction, the gateway to “getting to know her”. But that’s all that is. You would never use a corny line like that and then segue immediately into “Can I take you out? What’s your number?” But it might be enough to suggest, say, a coffee right there in the bookstore while you chat about authors or books that you both enjoy – or not. (I have actually made some of my best first impressions through friendly, humorous, satirical and parody arguments, more than through searching for points of agreement – but it’s a developed skill that I would not counsel that you lead with. I think the thing that has worked for me in those cases is demonstrating that I can argue and still be friendly and respectful, to show that I listen to what she’s saying and respond to whatever that was, to show that I do have a sense of humor and playfulness, and that I don’t take unserious things too seriously.)
It seems to me from your questions that you’re having problems with the meet-and-greet, which is tough enough, I will grant. But if you press too soon on the meet-and-greet then you’ll come across as desperate, needy (or worse) and not at all attractive. You can’t rush these things.
So, difficult as it is, I think you need to work on your skills in smiling and saying hello – just that for now – and then build up to another gradient step after that, “getting to know each other”, long before you even think of asking for a date. The process of getting to know a potential date isn’t the same as sex, but it can be a lot of fun in its own right.