A lot of that will depend on what the court decides. Indaba is a local supervised visitation facility. They charge about $65 an hour, but their rates may have increased. You should try calling them.
There are many providers in King County. You could check http://www.familylawcasa.org/supervised-visitation-services/ for a list of King County agencies. If you are not in need of a facility, then many providers offer services in the community that range from $40-$50 an hour. I also have an agency, www.childrenfirstvts.com, should you like to discuss options.
I agree with the prior answers, but people often forget that the court can also order that an agreed upon or court appointed person can be the supervisor. If this happens, we typically have the supervisor sign a document setting forth that they will be the supervisor and subject themselves to the jurisdiction of the court. The supervisor should be informed of what they are to supervise, the concerns (no disparaging remarks about other parent, no discussing litigation, etc.), whether it is to be "line of sight," what happens if the parent violates the terms (reminder, stop visit). I have had this arise to decrease the stress on the child and keep the visitation with a familiar person and place. If done right, this can be a wonderful alternative. It really depends on the people and facts involved. I hope this helps.