If the bark is not wet and is dried out good then yes it's fine to throw some wood bark on a wood stove fire.
I put my wood bark in a box or bucket and then bring them inside as I need them.
I throw a few pieces of wood bark at a time on the other wood that's burning and it helps to keep the wood stove going and to heat up the house.
Wood bark is wood and although it burns fast it still throws some heat out.