She kept hassling Harry about it, why didn't she try?
Dumbledore told Harry that he had to get it personally. Hermione trusts in his instinct that anyone else attempting to do it is doomed to failure and may well make it harder for Harry to get it in future.
‘I’m telling you, the stupid Prince isn’t going to be able to help you with this, Harry!’ said Hermione, more loudly. ‘There’s only one way to force someone to do what you want, and that’s the Imperius Curse, which is illegal –’
‘Yeah, I know that, thanks,’ said Harry, not looking up from the book. ‘That’s why I’m looking for something different. Dumbledore says Veritaserum won’t do it, but there might be something else, a potion or a spell …’
‘You’re going about it the wrong way,’ said Hermione. ‘Only you can get the memory, Dumbledore says. That must mean you can persuade Slughorn where other people can’t. It’s not a question of slipping him a potion, anyone could do that –’
Harry Potter and the Half-Blood Prince