The first thing I noticed is the knights seem to be darker than the other white pieces. The rooks show they are striped. So, any bleaching should be taken with consideration to this because wouldn't it still looked striped?
I can't post links but on Youtube, I found this "Yellow Wood Stain Colors and Polyurethane Using Yellow Dye Powder From Keda Dye With Polyurethane".
You can search it there and the idea would be to find something like the yellow stain formula. Maybe you can find something more between a yellow and white at a hardware store.
I’ve had this set since my early teens. The white pieces have darkened over time. I think this is a property of the wood since an elderly guy at a care home I used to go and play chess with as a kid had the same type of set and had the same problem. He bleached the white pieces but that was pretty drastic!
Any suggestions how to lighten the white pieces would be greatly appreciated!