npm script, copy package.json to dist when bundling

The syntax should work (and seems to, looking at your comments). I would suggest splitting your npm scripts across multiple points, though:

{
  "bundle": "NODE_ENV=production webpack --output-file bundledFile.js",
  "copy": "cp package.json dist/ && cp README.md dist/ && cp .npmrc dist/",
  "build": "npm run bundle && npm run copy"
}

In order to be cross-platform compatible (cp is not typically available on windows), I would also suggest adding a build file somewhere such as ./tools/copy-distrubution-files.js which would make use of fs to copy the necessary files, then call it in the npm scripts with node ./tools/copy-distribution-files.js. That will be (mostly) platform independent (you still have to assume that node is available as the nodejs executable, but that seems fairly reasonable to me).