I built my own bandsaw mill about 20 years ago from scratch. There's three different circumstances that apply. There's straight grain, wavy grain and interlocking grain. You cannot cut from a wavy grain tree without grain violations. You can cut from straight grain trees with, or without, grain violations depending on how you orient the cut. For bow work, to cut following the grain for many smaller trees in your first good slab (which have the most knot free wood), you cannot just slab cut, you have to take into account the taper of the tree and cut parallel to the top edge of the log. You may have to wedge the log to get there. Then if you turn it to get a good outer board from the other side, you also have to wedge that. Larger logs tend to be less tapered, so straight slabbing for straight grain works better.
The thicker the slab, the more you can do with it to get bow wood after it's been cut. You can follow grain that runs off the side of the board by ripping in that direction without a fence, just following a line drawn parallel to the grain. After that with a slab over 2" you can rip out parallel grain backing quality strips of that width. That would be done with dry wood and a planer blade.
The third case is with wood with interlocking grain. Two I can think of where it's common are elm, and yellow birch. Often there is no way to slab these without grain violation, but they tend to hang together anyway because it's as if the wood was braided internally like cordage. I don't know whether these would be suitable for backing material with interlocking wavy grain but elm does sometimes work for selfbows even though there are grain violations, rather than following the grain along the outer edge of a stave.
The above are all generalizations, and specific cases can and do vary. But for sawing, that's what I find when shooting for straight grain with minimal wastage.
