A PA28 pilot reported an airborne conflict with another light aircraft on a short flight from BED to BOS. The crowded airspace was a contributing factor.

Narrative

I was the second departure in a series of four: another piston single; me; followed by a turbo prop and a small jet. I was on an instrument flight plan and cleared to depart Runway 29 with a left turn to 250 issued at the hold line. The Tower alerted me to traffic in bound traffic for the left downwind. I departed and; at roughly 1;100 MSL; I initiated my left turn to 250. BED Tower then gave me an immediate hand-off to Boston Approach. As I was tuning the radio to 124.4 I lowered the nose to check for traffic. I then saw a [high wing light aircraft] zip by at roughly 500 FT horizontal distance and roughly 150 to 200 FT vertical distance. The [other aircraft] didn't appear to have taken any evasive action. I did not either; as we were on nearly orthogonal courses. Neither Bedford Tower before the hand off nor Boston Approach after the hand off called any specific traffic. On my departure I never had the downwind traffic BED Tower called out in sight. I also never told them I had the traffic. They passed the traffic alert with my departure clearance while I was still on the ground holding short of Runway 29. Despite being a flight instructor; and having reminded trainees on many occasions that departing an IFR flight plan doesn't relieve the pilot of full traffic awareness when in VMC; I allowed my focus on IFR procedures during a VMC departure from an unfamiliar airport to interfere with and reduce the amount of time I spent looking out of the windows for traffic. I was focused on my vectors to the BOSOX Intersection; the hand off to Boston Approach and not enough on looking for traffic. I am glad that I lowered the nose and took a look; but overall my eyes were inside too much. Also; as I have told many trainees; the pilot workload is higher for an IFR departure in VMC because you have to do all the IFR cockpit tasks; but also all the VFR traffic avoidance tasks. I am lucky that we missed each other. This experience is a valuable personal teaching moment and one that I can use constructively with my students.