Pet store bone has not been prepped for use as carving or inlays. It has usually been cleaned up enough that it looks nice, sometimes bleached with chlorine bleach, and pressure cooked with "flavors" so dogs will like it. It hasn't been degreased, and this--and the possible use of chlorine bleach--will often cause problems down the road.
If what follows seems like a long process, or a lot of work, keep in mind you can purchase properly-prepared bone for knife scales, etc from many of the suppliers. Crazy Crow is one source, or the various luthery suppliers. Thin bone for inlays can often be sourced from piano repair suppliers, as bone is now a common replacement for damaged ivory piano keys.
Basic bone prep starts with the raw bone. For a lot of stuff you can hit the local butcher up for a soup bone, or better yet, for a whole leg bone. Have the butcher cut off the ends (or do it yourself with a hacksaw, etc). Punch out as much of the marrow as you can, then scrape or brush as much more out as you can (old bottle or test-tube brushes work great here). Simmer the semi-cleaned bone for about 45 minutes in a mix of ~2 gallons of water with 1/2 cup ammonia and 1/2 teaspoon or so of Dawn dish soap. (Do this OUTSIDE, or under a really really good exhaust fan.)
Remove the bone and allow it to cool to room temperature. Don't try to accelerate the cooling by plunging it into cold water: this will sometimes cause cracks, and some will seem to show up about the time you are polishing your finished product. DAMHIKT.
Once the bone is cool, use a stiff brush and scrapers to remove any remaining soft tissue. A stiff nylon brush is probably best, but I have used brass wire brushes. Stainless steel brushes will score the bone, possibly enough to make it unusable for your project. I usually use a nylon "toothbrush" from the auto parts store, and a couple of scrapers made from bamboo skewers. The bamboo won't damage the bone, and I can throw them away when done. Once cleaned of residual soft tissue, let it dry for a few days to a week.
Next comes de-greasing. The usual approach here is to soak the bone for a 2-3 weeks in white gas (everyone I know uses Coleman fuel). Most folks soak in a (closed) glass jar. I usually cut the bone down to "blanks" (rough cut knife scales, turning stock, etc) before degreasing. Depending on container and bone size, you can usually soak 2-3 bones worth of blanks in a quart of white gas. Store your soaking container outside in the shade, or at least in an unoccupied outbuilding away from any source of ignition. . . because, well, it is a breakable container of flammable liquid.
When the gas gets discolored (takes on a brownish tint), grease is dissolving out of the bone and you need to change the gas. Dispose of the greasy gas appropriately. After a couple-three weeks and at least a couple changes of gas, remove the bone from the gas and allow it to dry in a safe place. It will usually dry in a bout an hour. If it takes longer, or if there are translucent spots that seem to shrink, the bone still has grease in it: back to soak in more (new) gas.
If, after working the bone to whatever your end product is, you feel it needs to be bleached, don't use chlorine bleach: the bleach will cause the bone to begin breaking down. Instead, use hydrogen peroxide from the drugstore (3%, IIRC), for no more than 10-15 minutes. If you leave it in the peroxide for too long, it becomes "flat" and looks like someone rubbed white shoe polish on it.
Some further thoughts:
What I described above isn't the only way to do it, but it is a common approach that has been generally successful for 100 years. In theory, something like lacquer thinner might substitute for white gas. Everyone I know who has tried it goes back to white gas; in my own experiments lacquer thinner took longer to de-grease the bone, and cost more.
Thicker bone (we're talking mammoth leg bone here, or shinbones from draft animals, etc) will take longer, and more changes of white gas. The times I've tried, mammoth bone seemed to take forever to de-grease. I guess it makes sense that the grease would have thoroughly-penetrated the bone in the thousands of years it has been sitting in permafrost, but it is a pain to work with.
Don't use the "greasy" white gas in lanterns or stoves. It creates an incredibly foul smell and clogs up the burners. (But it was hilarious to see the guy who called me "wasteful" try to explain the results to his wife!)
My limited experiments with stronger concentrations of hydrogen peroxide to bleach bone seemed to show no real improvement over drugstore concentrations, and higher concentrations did cause some degradation of the bone if left long enough.
