The immigration department admits asylum seeker boat arrivals have already exceeded government forecasts for this financial year.
The arrivals amount to a total of 12,884 people, while the government budgeted for 12,000 for the entire year to June.
Liberal senator Michaelia Cash homed in on whether more were expected to arrive in the remaining four months of the year.
"So, no one else is going to arrive from now and the end of June - is that the prediction?"
Senator Cash, who was questioning Mr Bowles at the hearing in parliament house on Monday, also pointed to figures released as part of the additional estimates process.
These showed costs for asylum seekers had more than doubled this financial year, from the government's forecast of $1.1 billion in the May budget.
He said the department was changing the way it was processing asylum seekers and moving more people out of detention.
"If we actually see more people arrive, but move through the system more quickly and into bridging visas, for instance, as one example, we might actually see a reduction in the overall spend," Mr Bowles said.
The figures released as part of the additional estimates process show the government expects costs relating to its asylum-seeker policy to fall from $2.23 billion in 2012/13 to around $340 million in 2015/16.