I suspect by 'grain' runout you actually meant growth ring runout? Regardless, I'll answer regarding both radial grain runout and ring runout.
First of all, it's difficult to do by way of store bought, or 'incidental' lumber since it's produced with entirely different requisites in mind. I've done it, searched through mountains of beautiful hickory and hard maple lumber and felt like I really accomplished something if I left with even a single piece. But even then, aside from the 'grain' issues, I always have doubts in the back of my mind about the tree selection and its treatment between felling and drying.
The best ways I've found to better the odds of straight radial grain and growth rings is either A.) buy from a supplier/sawyer that is a bowyer himself, or one sympathetic to a bowyer's needs.(and even then I've learned not to trust them 100%) or... B.) choose a tree myself that has the qualities needed, have it sawn into oversized lumber to produce the most and best possible grain and ring orientation, dry it and then reduce it and resaw the backing strips myself with the same requisites in mind.
I recently cut two big pignut hickory trees and began to envision the orientation of the backing strips, and a few staves within, before they hit the ground. Once down, I strategically planned each and every cut, beginning with how far I made the first cut from the butt swell(running a butt swell through a sawmill means ring violations), and including each cut made at the sawmill(I was 6' from the blade directing the sawyer as he positioned the log for the cuts), so that I maximized the amount of wood I would get with near-perfect straight grain and ring orientation.
I undoubtedly got a LOT more pieces for backing strips than would have been possible if I wouldn't have formulated a plan with him prior to 'cut day', and hadn't been there in person at the mill... than if I trusted him to understand and do what was best for the bows on his own. I also got some very nice wood for cores, lams, even several nice staves fell out from between them all(Plan the work and work the plan
I KNOW that wouldn't have happened without my presence. But even with all of that attention to detail, there's only so much you can do. As good as it looks now drying in my garage, I expect considerable future loss due to 'the process', but I think we did the best we could have done with them to this point.
The nicest looking trees on the outside are rarely perfect on the inside. When it comes to these backing strips we'd like to have with perfect grain and rings, the pickier we are about it, the less material we net as a result, but I'm ok with that because I want to be confident in the material I use for my bows and their durability afterwards.
To more directly answer your question perhaps... in order to cut backing strips with minimal radial grain runout, the tree must have VERY straight radial grain to begin with... there's no fixing or avoiding it. Then depending on which cut being made, it must be sawed parallel or perpendicular to that grain at the sawmill... and again as we resaw it at home. Picking the absolute best tree for the task though is Job #1, and MUCH of the balance falls into place following that.
In order for there to be no growth ring runout, the section of the tree used must be of a consistent diameter, straight, oriented with the rings as parallel or perpendicular as possible to the blade for each cut, or ample room left to do so at home, and dried properly to minimize warpage. Perfectly straight grain won't be straight in the end if it warps. And, toward that end we should choose a 'neutral-growing' tree, growing straight up and protected from prevailing winds and other factors, with minimal differences in tension and compression sides as this too helps minimize warping as it dries. Again, Job #1 is proper tree selection. With it, many pitfalls are avoided.
I better stop there... Sorry that was so long...
