Reddit mentions of The Art of Turned Bowls: Designing Spectacular Bowls with a World- Class Turner

Highly recommended, well worth the money:

The Art of Turned Bowls by Richard Raffan

There are a lot of books, DVDs, and YouTube channels that go in to how to turn a bowl and comparatively few that go in to what makes a pleasing shape. This is one that does and if I could pick only one woodturning book to own, I'd be hard pressed to choose between this one and David Ellsworth's book.

The curved tool rest isn't necessary until you start making larger deeper bowls (and still not necessary even then according to many well known turners). It won't help you develop flowing curves; it doesn't help guide you or work as a template.

I'm trying to think of technical points that helped me break out of the "dog dish design" phase and it's hard to think back to everything that contributed. I might have to keep thinking on this for a while and come up with a post for you all.

One thing that does come to mind is the importance of moving "from the hips." It's easier to create a flowing curve (on the outside) if you are keeping your arms relatively locked in place and moving smoothly from weight mostly on the right foot to weight mostly on the left, as opposed to trying to move your arms. For any of you that have studied Tai Chi, it's very similar to that.

An additional point on the above is you want to start uncomfortable, finish comfortable. When people first start making curves by shifting their weight from one foot to the other and moving from the hips, they often come to the end of their comfortable range of motion before the curve is complete and then finish awkwardly. Instead, you want to plant yourself in a comfortable finishing position first, then back off the weight to the other foot to start the cut, which will probably lead to you feeling a bit uncomfortable at the start but trust me it's better that way.