Try everything on a piece of scrap first, because there is a lot of good advice in this thread.
There are several tricks I have learned from far better builders than I am. I learned by putting a bone inlay in the wrist of every one of my guns ( all twelve of 'em).
The first is that the bottom seating of the inlay to the wood should be flush, so a delicate hand is called for. The second is is not to be put off by a lot of bone sticking up out of the epoxy well it is seated in.
Be careful not to overload on the epoxy because too much of it will corrupt the surrounding wood to the stain. I was taught to use Coffee stirrers as spatulas, and to get excess off quick when I clamped the inlay into the wrist mortise. The excess epoxy will come off when you sand and whisker.
Rubber clamps only...or at least thorough padding so as to avoid marring the wood or bone
After smoothing and whiskering, but before staining, coat the inlay with rubber cement. Cut the hairs of a fine brush really short so you can stay within the border of the inlay with the cement. You can go right over it with stain that way, but you need a steady, gentle hand.
If you want to antique or stain the inlay, then do it after you have assessed the final color of the wood....maybe ivory white, maybe yellowed....you'll know.
When you oil the stock, you can decide whether to cover the bone also.
Good luck...
Capgun