Vice President Bush may be narrowly trailing Gov. Michael S. Dukakis in the opinion polls, but he is far ahead according to another indicator of Presidential prospects: the ''royalty factor.''

''Going by the statistics of the past, Mr. Bush will be the next President of the United States,'' said Harold Brooks-Baker, publishing director of Burke's Peerage Ltd., the 162-year-old directory of British nobility.

Burke's Peerage today released a report tracing the Vice President's family tree to the 1400's. The study by Burke's senior genealogist, Roger Powell, and an American colleague, William Ward, found that Mr. Bush has more connections to British and European royalty than any President of the United States. Queen's 13th Cousin

For example, Mr. Bush is a 13th cousin of Queen Elizabeth II and is related to all members of the British royal family, according to Burke's genealogists. Moreover, he is related to all those who have married into the British royal family, like the Queen Mother, the Princess of Wales and the Duchess of York. Mr. Bush is also related to all current European monarchs on or off the throne, including the King of Albania.