The Judge will issue a warrant for your arrest on the day that you fail to appear for the hearing. The warrant will remain outstanding until you are arrested by a law enforcement officer or you set a hearing to quash the warrant. Generally, the police will not actively search for a person that has a DUI warrant but you will likely be arrested if you have any contact with a Washington state police officer. You should attend all court dates and contact an attorney to discuss your case.
If you fail to appear for a scheduled court date the judge will have the option to issue what is called a "bench warrant" for your arrest. You can determine if a warrant has been issued by calling the court clerk of that particular court and asking them to check. If one has been issued, you have a couple of options. You can set a motion to "quash" the warrant, which means you can ask the judge remove it and set a new court date for you (which is up to the judge's discretion) or you can either post the entire amount of bail or have a bondsman post a bond, for which you will generally have to pay a 10% fee.
A warrant is issued for your arrest and you can be arrested next time you are pulled over. I would go to court with an attorney and just take care of it. It certainly is not the crime of the century.
Any time you receive a summons to show up in court, the judge will be expecting that you appear in a timely manner. A failure to appear will likely result in the judge issuing a bench warrant, and the next time you have any contact with a law enforcement officer you could be taken into custody because of the warrant.
It is also important to keep in mind that many times having an FTA in a criminal case against you will result in harsher conditions of release being imposed once you are finally brought before the court.