The Open Public Meetings Act (OPMA) applies to the “governing body of the recognized student association”. RCW 42.30.200. http://apps.leg.wa.gov/RCW/default.aspx?cite=42.30.200
The Board of Directors is the “governing body” and therefore they are subject to the OPMA. You may record their public meetings without needing to request permission. RCW 42.30.040 prohibits conditions upon the attendance of public meetings. http://apps.leg.wa.gov/RCW/default.aspx?cite=42.30.040. My office has construed the prohibition of recording devices as a “condition” upon attendance. You only need to ensure that your recording is not disruptive. A member of the public may not reasonably object to privacy concerns since the meeting is public and open to all to attend. Any objections should be ignored since the law clearly prohibits conditions to attendance.
Ultimately, where a violation of the OPMA occurs, you the citizen must enforce your rights. There is no state agency that enforces the OPMA. It is enforced by filing a lawsuit in court. RCW 42.30.120, 130. If you prevail in court, then you are entitled to reasonable attorney fees and costs.
Here’s a link to the formal opinion by the Attorney General which concludes that the public may record public meetings. http://www.atg.wa.gov/opinion.aspx?section=archive&id=9332