Hello XXXXXX,
The answer depends on where the bench warrant was issued, for what and if the warrant is in the same jurisdiction as the airport and if you are flying international or domestic.
You can be arrested anywhere in the jurisdiction covered by the warrant. If you are trying to leave the country and they run your passport or driver's license and the warrant comes up the person will certainly be arrested.
It would be unlikely, but again it depends on the reason for the warrant. If you didn't show up for jury duty they can issue bench warrants. Most people don't even know they have bench warrant for not showing and then bam they get pulled over for a traffic stop and learn the hard way!
However, I am not recommending you do anything illegal. If its at all possible take care of the traffic violation prior to your departure and you won't have to worry!
Safe trip!
Attorney
General Practice, Wills, Probate, Family, Bankruptcy