I have changed my code to the following. I'm somewhat more confident now I understand the code a little more, but won't have a chance to test it for another 12 hours.
cameraname is a string of the camera's name I want to trigger. BIserver is the fixed local ip of the bluebirds server.
void triggerBI() { // sending the trigger to Blue Iris web-server
WiFiClient client;
if (client.connect(BIserver, 818)) { //Port number of the Blue Iris web server
// Make a HTTP request:
client.print( "GET /admin?camera=");
client.print(cameraname);
client.print( "&trigger");
client.println( " HTTP/1.1");
client.print( "Host: " );
client.println(BIserver);
client.println( "Connection: close" );
client.println();
client.println();
client.stop();
}