Was George Bush and George W. Bush father and son and elected for us presidents?

Yes, they were the second father and son to serve as U.S. President (1989-1993 and 2001-2009). The first were John Adams (1797-1801) and John Quincy Adams (1825-1829). Also, William Henry Harrison (1841) and Benjamin Harrison (1889-1893) were grandfather and grandson.