Okay. I can tell you what I would do in that minor, but important, situation. I'd cut a small framing shim and make several small ones. Slide them into the gap where a 'bush' can be set over them, and press or withdraw to adjust. It'll work.
I am not looking to move the whole bridge, it is hinged at the right side and not adjustable. I just hope to move the rails on the ties horizontally, a couple hundreths of an inch, as the room warms or cools and the rails get out of line.
I did not do as you describe, so no pix or link from me. However it sounds like you'll need an L-bracket that one might find near a corner of a cabinet...maybe. Hardware stores carry them, chromed, about 4" long, or 5". They'll have holes drilled in them. I would place the long shank of the L in a channel, maybe, screwd into place, and then use a long machine screw through the small shank's hole to move the bridge closer or further away as needed. Is this what you're talking about?
In my case, my bridge lifted out and sat on two small wood screws. Its abutment was cut to shape to slide it into fairly snugly. The bridge also had two small wood screws as its 'shoes', and they sat on the wood screws below, in the bearing plate of the abutment. This way, I could back out or screw in any four screws to adjust for my double track gaps across the bridge ends. Minor horizontal adjustment was by nudging.
The wood screws all had feeder wires wrapped around their shanks, thus affording continuity up to the bridge rails.
I have briefly seen pictures of a method of moving the track horizontally at the end of a layout gate using a screw attached to a tie and anchored at the head end of the screw. I would like to see in detail how this was done, how the anchor works, the screw is attached to the rail, and where I can get these parts.