She and I both did all that. And tried macro mode. And zooming in. And googling like crazy. After a lot of research, I realized that because of the small sensor on the camera, you really can't get the effect unless conditions are just right and the background is really far away (well, relative to your subject). You can get it in some cases, but those situations just weren't really the type of things she wanted to photograph.
Here's a review of the SX520 that calls out the issue. I found others that said the same thing when I was researching it, but this is one I could find again quickly. The sensor size is still the same on the SX720/730:
http://cameradecision.com/faq/is-the-Canon-PowerShot-SX520-HS-good-for-Portrait-Photography?
I spent quite a bit of time on this, because DD was bugging for a DSLR at Christmas, and I wasn't convinced she had max'ed out the abilities of her Powershot yet and was ready for something more. But in working on it with her, I realized she had spent a lot of time already trying to get it, and could talk about aperture and a bunch of other topics quite intelligently and it was time for her to upgrade. So she got a Canon T7i for Christmas. She's now the photographer of the family. I'm still more than happy pointing and shooting mostly in auto mode - blurry background or not