Is "After a bill has been passed, the Presiding Officer of the Scottish Parliament submits it to the monarch for royal assent after a four-week period, during which the Advocate General for Scotland, the Lord Advocate, the Attorney General or the Secretary of State for Scotland may refer the bill to the Supreme Court of the United Kingdom (prior to 1 October 2009, the Judicial Committee of the Privy Council) for review of its legality." a good answer to the question "In Scotland, who is responsible for submitting a bill for royal assent?"
yes