You can find vintage parts on eBay - if it's an older White (not one made for Sears that copies Singer) it will take a shuttle with a pin in the middle, and the bobbins are hollow.
they are not one of the cheaper shuttles/bobbins to be had though, and if you find the shuttle for under $20 you are doing good.
One time I found an old White for $10. I bought it and my husband asked why - because I needed the shuttle and that was one of the cheapest I'd found.
I've also managed to pick up several tucked into attachment boxes, but unless you can get a good picture, there is always the risk that a shuttle in a box marked "White" is not a White shuttle.