Not being funny but it may be easier to make up the bellows complete in heavy paper first to see if your design works well, folds down small enough, fits the body, ect. Then you can cut one corner to lay out the fabric.
"I haven't decided yet. I suspect the 1-by-1 is actually easier although more time-consuming. The block would seem to take more planning and be more prone to major screw-ups. (I can easily re-cut a single strip as opposed to an entire block.) Do you have any preference?"
Yes, I prefer to do it in a block. Drawing it all out on fabric and lining it up is a pain, it stretchs. Drawing it out on a large sheet of poster paper and laying it out in one piece is easier and everything is aligned the first time. Just use 2 full length dowels to hold the pattern off the fabric until it's lined up and set down the center, pull out 1 dowel to set that side, then pull the other and set it.
(This will take longer to read than to do, and it works out well. Great looking bellows the first time.)
To do it in a block you will need a steel straight edge, 1/8" paper punch, a poly cutting board and a 2 bladed knife. The knife is a standard non-retracting utility / sheet rock knife modified to take 3 blades: 2 sharp and the center spacer with the tip chipped off. You do have to shave the inside of the handles to make them fit right, you will see where. It take longer to write it than to do it.
Lay out the pattern complete on the poster paper. Punch the 1/8" holes 1/4" in from the edge on the fold lines. Connect the holes with the straight edge and knife, this will make a 1/16" slot on the fold line. The point is to leave little tabs that hold the ribs in perfect spacing and alignment so don't cut through the tabs.
Lay out the panels on the fabric and mark top, bottom and side with tailor's chalk. Set the top panel first. Align the fold lines of the side panels to the top panel and set. Do leave 1/8" space between the sides of the panels, closer will put too much strain on the corners when folded. Align the fold lines for the bottom panel to either side panel and set. If everything looks correct, glue on the inner lining. The only real pain is the inner seam but you have to deal with that either way you make a bellows.
IF you aligned the fold lines and IF the spacing between the panels is straight, the bellows with fold-up easily the first time. It will also look PERFECT.
Apologies to Camerabellow.com