Input bias current existing even when no input is given
but in proof they put both the voltages at ground and they were still considering input bias current.I'm a little confused that even when there is no voltage at input from
  where the op-amp is drawing current?


Consider the LM324's equivalent circuit: -



If either input is grounded or taken to the negative rail then current will flow from the base of Q1 and Q4 to the tune of about 45 nA.