I use oxalic acid to bleach wood and it works well.
I won't use laundry bleach though it will lighten wood to some extent. The sodium hypochlorite in laundry bleach is a very strong oxidizer and any hint of residue left in the wood combining with moisture will coarsely rust the steel.
I know,,some will say they have used it for years with no bad effect,,,some also say salt wood is OK too. Same idea
Wash your gun cases with a little bleach and store your fav SxS in it for a while then see how well it looks.

Anyway,,,Heat the soln of oxalic acid crystals and water (I use a couple tbsp in a qt of water) in the microwave for 45seconds or so then apply w/a brush. Or if the container is wide mouth enough or the part is small enough just stick it right in the stuff.
Used cold or room temp won't get too much results.
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Use a clean brush to agitate the stuff and brush it around the surface of the wood.
It'll sting your hands if you have any cuts on them and surely not feel good in your eye(s) at this concentration so be careful.

Let it set on the wood till you get the result you want, then rinse with clean warm water, again simple brushing to clear the stuff from the wood.

Careful with the wood as it will bruise easily when wet. Comes back to full strength when dry which doesn't take all that long. I let them dry naturally, but you can speed dry the surface with a propane torch quickly, just don't scorch the edges.

The wood will be clean, grain raised, especially if you give it a once over with the propane and ready for a light sanding. Many small dents will be lifted from the warm water.
The wood will now take stain evenly. I like to start with alcohol stain first and use oil based stain later in the finishing process but every one has their own way about it.

Bleaching is useless w/o first removing any oil embedded in the wood. That has to go.

All sorts of discussions of how to do that are around.
The oven cleaner method will clear oil & grease from the surface and just below it very well.
I recommend wood bleach after that to even up the sometimes odd coloring left behind by that method.
Deep embedded oil needs more work to remove. I do use lacquer thinner soak sometimes, but always follow up with whiting powder to draw out the last and deepest of the oil in the wood.
It's a slow process but it does work the best. Wear a mask when brushing off the dried whiting powder.