Yep, ivory, and other bone such as antler, has a grain to it just like wood. And it needs to be used with this grain in mind just like wood.
To the OP, grant1265. From the fuzzy pictures I'd say you're a better wood worker than photographer. The one of the grips on the gun is particulary fuzzy. The other of just the grips is better. You need to learn how to use the focus option. Or if using your cell phone how to light the subject until you almost need sunglasses to be in the same room when taking the picture!
Your workmanship looks pretty good from what I can see. But the wood itself seems a bit lifeless as far as grain goes. It also looks like the aspen is a softwood judging by the slight chewing around the screw holes.
So first off for your next project of this sort search around for a good hard wood to work with so it takes and holds the details and sharp edges well. Even if you're not planning on doing any checkering your choice will pay off with sharpness to the edges of the grips and the screw holes.
Generally, as a long time wood working hobbyist, I find that if I need stain to make the wood stand out that I've chosen the wrong wood to start with. The better woods for grips and stocks stand out on their own with just some oil or varnish finish and have grain that holds its own for color and appearance.
Keep in mind that this doesn't mean you need to shop in some exotic wood emporium to find good wood. The pallet wood used by El Mariachi above shows what you can find if you keep your eyes open and attentive.
Please don't see this as in any way negative. You did a great job on those grips. My thinking is to encourage you to look around for other woods and experiment a little for your next project so they really SNAP much like the grips seen in RCModel's post. Such stuff is out there. And with some knowledge of what to look for can often be found in the firewood pile if there's an assortment of hardwoods present rather than the usual garden variety softwoods.
Even passing by a gang chopping down old trees can often land you a hunk of apple or other fruitwood for the asking if that's what they are chopping down. I've got some wood turnings I did using wood from an old deseased apple tree that are wonderful for their colour and grain.
Be warned though. You may be wandering into a whole new hobby if you take the bait...