Instead of changing the size of the opening, use a pair of 24" doors in the "bypass door" configuration. They'll overlap 4" when closed and you'll have a 20" opening when they're open.
If you want to increase the 20" opening, you can cut the doors to make them narrower and this will still be less work than changing the size of the doorway. Even garbage MDF doors can be narrowed almost an inch on each side, especially if you're not attaching hinges or real doorknobs.
Your idea about the 1X6 on either side is a good start. It would give you something to fasten to, in a simple fashion on both sides, although the fastening would be minimal. You may need to increase the number of nails in the jamb to keep it in place over the long haul. Same thing if you use screws.
When the 1x6, for a 6" wall, or if it fits, 1X8 for an 8" wall, is set in place, use construction adhesive between the block and 1X and let it harden. Make sure your block are clean so the glue sticks. This will give a firm base to work to. Do not skimp on the glue. Use a 10 oz tube, a half tube at least, on each side before you set the 1X. Use concrete screws to fasten it in place, they are more reliable for a first time installer. You could use masonry nails but there are places they may not hold. The screws may fail in their holding, but that will be obvious. To increase the chances of holding, use the screws only in the block, not the joints. Keep the screws about an 1 1/4" to 1 1/2 from the edges of the block. The block is thicker there and is far enough from the edge to keep from cracking out (should be). Screws also only affect a small area when they fail, nails break out larger pieces.
To answer the other part of your question, yes you could use framing only on one side, them shimming and fastening the other side is tricky. There are case hardened finish nails to do this, or even screws. For a first timer, what I mention above should do what you need.
Best Answer
Beth, If your referring to an opening not intended to ever have trim, consult the rough opening (RO) parameters of the bi-fold door manufacturer, as the type and placement of the hinge pins and the thickness of the door will determine the space needed between the outer edge of the closed door and the frame of opening.
Most bi-fold doors are about 3/4"-1-1/4" thick (depending on if they're made of PVC or wood and solid or slatted...older, reclaimed doors are thicker). If the hinge pins are set half a thickness in from the outer side edge of the door, the clearance will need to be about 75% of the door thickness...especially if the door frame isn't perfectly square or hinge pins aren't set perfectly perpendicular to each other.
I'm working on a set of bi-folds that are 1-1/8" thick and require a min. 1/2" clearance between door and door frame (which doesn't give much leeway for error); where the doors meet there isn't supposed to be any space...they're meant to be flush to each other...but I'm adding an astragal, to one of the doors, to make installation easier and look more finished.
If you the doorway opening will, eventually, have trim decrease the RO width by 1-1/2" (assuming trim will be 3/4" thick each side).
If you know the floor is level; with no rug in the way, I'd give 3/4" for a space in top and bottom...some like it 1/2" but in adjusting the doors, after installation, sometimes that extra 1/4" is useful.