I recently completed this commission for a goose-inspired bowl in walnut. In some ways it may seem to be quite a departure from a “regular” bowl form, but the process is essentially the same. As is typical, I work with a basic layout on top of the log indicating the interior edge of the hollow and the line of the outside edge (also on the bottom). Then I hew and carve away the material between the outer lines of the top and bottom by hand and eye.
To establish a symmetrical form, I usually rely on a compass. Even a form like this stylized goose begins with a few compass arcs. Playing around with a compass reveals all sorts of possibilities. If nothing else, it helps guide some freehand layout.
In the photo below, you can see the basic idea. This is not the exact layout for the bowl in the photos. Every log is different, so each bowl gets laid out directly onto the log. I’ve only drawn it on paper as a demonstration. The black lines are compass-struck; red are drawn. The same concept can be used to layout any bowl form if you are seeking symmetry.