If this is a shootin' gun, then bed the action and be done with it.  If it's a lookin' gun, you can do this with epoxy bedding.

Get a roll of 10 mil PASCO pipe wrap tape.  Wrap the barrel with one or two wraps or whatever gap you want, prep the stock, apply mold release to everything you don't want to glue into the stock, and then apply the bedding compound of your choice.

Cut the ends of a handful of popsicle sticks to an angle.  Use those to make a nice filleted joint along the epoxy line between the stock and the tape.

Let 'er set awhile, then pop it apart.  If you did it right, there will be no voids under the barrel.  If there are a few invisible voids, don't sweat it.

The epoxy can be tinted to match, or not.  A tint that is the same color as the stock but not quite as dark is less obvious.  I use artist oil paint; only small drops are needed, don't over do the color.

On the other hand, a contrasting color such as red on black would be cool.