The original bill was to be voted just as the war ended and it included a critical detail: female military draft. The world war 1 machine was running out of men to send to the war and the volunteer system for women did not turn out enough people to fill the ever increasing demand in the war factories. Something had to give.
Creating a female military draft raise some major concerns in 1918, one being that women had not voted to enter the war in the first place. It was seen as a bit unfair to then demand them to help fix the situation. Thus the right to vote.
Then the war suddenly ended and the bill got postponed. The female draft part was dropped but the idea of women vote continued with force and a year later it passed.
Most historians agree that the world war 1 was the catalyst for the women suffrage movement, through there are some disagreement. Some points to the fact that the movement existed before the war, but how significant their political influence was at that point is far from clear.