A320 First Officer reports his Captain not taxiing via the cleared route while the First Officer is starting the second engine. Runway 4/22 was used as a taxiway instead of crossing it as cleared.

Narrative

At BWI airport given taxi instructions (pushed back from the gate) to Runway 28 'VIA PAPA; BRAVO; CROSS RUNWAY 22'. As I looked up from starting the second engine the Captain had already turned onto Runway 22 and was taxing to Runway 28 via Charlie. I asked the Captain where he was going and he then completed his left turn and proceeded north east on Runway 4/22. The Captain then turned right onto Bravo and picked up the rest of the taxi instructions. In my departure brief; (I was the pilot flying) I asked the Captain if I could start both engines prior to taxiing first flight of the day; heavy for an Airbus; and the busy nature of BWI in the morning). The Captain stated 'as soon as I start to move forward you can start the second engine'. During the push I started #1 engine and tactfully asked 'just start one'? The Captain again stated 'wait until I start moving'. After we were released from guidance; the Captain directed me to call for taxi. We received our taxi clearance and began to move. I then began to start the number 2 engine. The Company has pushed the single engine issue to the point where Captains are not exercising good judgment when and where not to employ single engine operations. As a retired Air Force Fighter Pilot I am not going to say that I can't do something/anything. If the Captain wants me to start the second engine and not assist during the taxi (during the start) then that's what I'll do. Bottom line we taxied a plane full of people down a runway without clearance. When I noticed it there was nothing I could do about it. I am not confident the Captain would have listened anyway. I strongly recommend more guidance be given to Captains about the COMMON SENSE issues associated with these unsafe single engine practices. I have to work too hard with too many Captains which could be mitigated if Company procedures were more smartly implemented.