The leaders said their concerns arose from a report from the Department of Transportation's inspector general.
"The report revealed excessive board spending on air travel, meals and wine," they wrote. "Overall, the report depicts an organization that conducts much of its business behind closed doors, awards many of its contracts on a sole-source basis and is in desperate need of reform."
The first phase of the Metrorail extension to Dulles is under construction and is currently scheduled to be completed by the end of 2013. The project has received about $900 million from the federal government.
The DOT has appointed an "accountability officer" to oversee the airport authority, and the leaders said Tuesday that the panel should cooperate with its oversight for the reminder of the project and beyond.
"We expect that you will grant her access to personnel and documents, and inform her in advance of, and provide access to, all board of directors meetings, including executive sessions," they wrote. "With her guidance, you must upgrade your procurement and travel policies, ethics code and bylaws, bringing them in line with best federal practices."
When the construction of the Metrorail extension to Dulles airport is complete, it will be transferred to the Metropolitan Washington Area Transit Authority (WMATA), which will oversee operation of the new railway.