1. I don't understand some questions left by the teacher, so I need to check the literature. If you are embarrassed to ask a girl out directly, you can tell her some questions left by the teacher last time, and you need to look up the literature, which happens to be unknown to her, and then listen to other students saying that there are similar literatures in the library. So since she doesn't know, she will definitely want to know, so if she is free, she will definitely go with you. This just achieved your goal, without saying it directly, without any embarrassment, and achieved the expected goal.
Tell her casually that there are books in the library that she has always wanted to read. Girls generally like reading books, and they read all kinds of books. Some books may not be available by yourself. If they knew that there were books they wanted to read in the library, they would certainly run away without hesitation. And don't just tell her that there are books she wants to read in the library, just say so. It can be said that she once went to the library and seemed to see the book, so she deliberately asked her if it was the book she had always wanted to read, or that she read a particularly good book in the library one day and then named it. Since she wants to read that book, she will be very excited. Needless to say, she will drag you to the library.
Tell her you want to buy a book, but I don't know what it is. Let her recommend it to you and take a look at it for you. You didn't ask her to go to the library, just asked her to help you. Generally, girls won't refuse others' help. They can do it themselves, and it is no problem to help others, so girls will be happy to help. And the real purpose is to ask that girl to go to the library, so anyway, it's good to go. When you get to the library, just ask her to help you read the information. It's up to you to buy or not. It doesn't matter if you don't buy it, just say you didn't see the right information. You can buy it. It will be useful to you anyway. After reading the information, you can go to the library to read again, without any problems, so the goal has been achieved and the girl will not say anything.
Actually, it's very simple to ask a girl to go to the library. There is no need to say it euphemistically, just say it directly. Girls have a natural love for the library, so they will be happy to go to the library. If you don't want to say it directly and feel embarrassed, then make a polite appointment.