I am not licensed to practice law in your State, but I will try to give some guidance. Unless the State of Washington is different from other states, the warrants never expire. I suggest that you contact the courts where the warrants originated to determine the amount of the bail. After you have posted the bail, the respective courts will schedule your cases for a hearing. It may be in your best interests to consult with an attorney licensed to practice law in your state to confirm that you are going about this the right way.
In Washington (and most States) bench warrants do not expire. They do need to be "renewed" after a period of years (usually ten) or they "expire" from the computer system. A judge can (and often will) renew the warrant for another period of years (again, usually ten). If the judge decides to not reissue the warrant it is still active, but law enforcement has no way of knowing about it.
There are a couple of things you can do to quash the warrant. Which option is the best will depend on the jurisdiction and the facts of your particular situation. You can always pay the bail or arrange for a bondsmen to post bond on your behalf. Another option may be to request a new court date from your court. Some courts post their procedures on their websites, others do not. Finally, you can always turn yourself in and ask for your release at your bail hearing (usually the next day).
A lawyer can help you figure out the best way to address the warrant and possibly arrange and resolution prior to your returning yourself in. Better to deal with this on your own terms, rather than wait until you are unlucky enough to get picked up. Usually Driving While License Suspended in the Thrid Degree is a fairly easy charge to resolve, especially if you have paid the fines and have been re-licensed.