Like Jim, I use plane jigs for this sort of thing. Mine may be a bit more sophisticated than his, and I use the same sort of setup to make rosette parts.
Take a piece of wood and glue a couple of rails to it just far enough apart so that your block plane will run in between them. Plane away at the wood for a while and the plane will stop cutting once it takes enough material off so that it's riding on it's side rails. Now, rout a pocket in that surface, and drop in a piece of bone or wood that sticks up. When the plane stops cutting the piece will be exactly the same thickness as the depth of the pocket.
I first saw this being used to make bone saddle pieces. I'd been trying to think of a way to shape pieces of wood to fit together and make a braid pattern, and this was the key. It's the technique that was used a hundred or more years ago to make bamboo fly rods: you make six triangular strips of bamboo and glue them together to form the hexagonal shaft. The strips can be tapered to an exact profile for the flex you need.
For bone tie block strips I will use a plane jig to thin out a piece of bone to the appropriate thickness. On edge is squared up on a shooting board, and a small hand saw is used to cut a narrow strip off the edge; a jeweler's saw works well. Then you square up the edge and have at it again. The strips are made a bit wide, and trimmed up with a file after they've been glued on.
I'll note that I've had much better luck planning bone with my old Stanley block plane than with the newer ones that have harder irons. The Stanley has softer steel which doesn't chip as easily, so it actually holds an edge a bit better. I put on a pretty short bevel for this (since it's a block plane the bevel is up, and there's no chip breaker). Then I put a small back bevel on the bottom at about 3 degrees which helps back the edge up better. You do have to touch up the edge from time to time, but it holds up surprisingly well.