The bill needs to be rejected twice before the government can use it as a trigger to have a double dissolution. And, I think there has to be a lapse of 3 months (could be 6 months, not sure) beyween the first rejection and second rejection.
So, the government really can't use the first rejection as a trigger. But, if there is already another bill that had been rejected twice in the past then it can use that one as a trigger.
There is nothing to stop the government calling a snap election for the House of Representatives and half of Senate.
