I'm trying to access the query string used by the client when contacting my service. How can I do this? 

You can access the query string through the HttpRequestMessageProperty.

OperationContext context = OperationContext.Current;
MessageProperties properties = context.IncomingMessageProperties;

HttpRequestMessageProperty requestProperty = properties[HttpRequestMessageProperty.Name] as HttpRequestMessageProperty;

string queryString = requestProperty.QueryString;