Long story, but I have a whale vertebra from the arctic as a surprise for a friend's husband (they are chiropractors - lol). This thing is rather weathered, and came from a hunting village in Fort Resolute, export permit and all. It's not new!
Anyway, it does need a bit of a cleanup. I found a really good site on this and I can get oxygen bleach, and the instructions are to mix a lot of the bleach (or 12% hydrogen peroxide, which I can't find in a large container) and top it up with water and leave the bone to soak in a plastic container for a few days.
Not sure I have a large enough container, but will check.
I had also thought of using a spray bottle of the bleach and a soft-medium brush to clean it.