Use a tape measure to measure the length of the beam.
Cut a strip of drywall track with tin snips to match the measurement of the beam. Multiple strips may be required for long rooms. If so, cut several strips to make up the total length.
Position the drywall track on the side of the ceiling joist adjacent to the I-beam with the open end of the track pointing down. Screw the track to the joist with wood screws put 1 inch from the end of the track to begin with and spaced every 12 inches down the track. Use a drill with a screw bit to drive the screws in place. Butt the ends of tracks together if you need to put multiple tracks to cover the length of the beam.
Measure the beam height from the base of the beam to the ceiling joist. Mark the height on a piece of hardwood sheeting with a pencil, and then use a straightedge to mark a straight cutting line along the sheet to create a strip of hardwood the exact same height as the beam. Cut the hardwood along the cutting line with a table saw. As with the track, if multiple sheets of hardwood are needed, cut enough to cover the length of the beam when placed end to end.
Attach the hardwood to the outside edge of the track, the edge away from the beam, using wood screws through the track and into the rear of the hardwood. Use screws that will not penetrate entirely through the hardwood, leaving the side that will be visible outside the beam unmarked. Space the screw placement every 12 inches. Repeat the track and hardwood placement on the adjacent joist on the other side of the beam.
Measure the distance across the bases of the two hardwood boards. Cut another set of boards to match the width using the table saw.
Place the newly cut board across the other two, passing beneath the beam, and screw it in place with countersink wood screws. Cover the screws with wood putty the same color as the hardwood to conceal the screw appearance using a putty knife. This will complete the bulkhead body, covering the I-beam completely.
Sand any exposed cuts with a piece of fine-grit sandpaper to smooth the edges of the new bulkhead.