How do you document bodges?

The modification is a proper part of the design of the product. So, no, don't "hand draw that on the PDF".

Add it to the schematics. You should have proper versioning control for your schematics anyway (Try git. It's thought for source code, but it works with any file type – you just won't get useful differences displayed between revisions, but that's not a problem here). Clearly annotate it in your schematics. If your EDA suite allows that, change color, stroke, whatever of the modification to make clear it's a modification.

If your modification is just a wire bridge: it's not uncommon for schematic design programs to have some kind of special "external connection" component.

Since you're probably want to still be able to generate a valid board from that schematic, make sure the "external connection" component you have has a small single pad that you can place on a wire in your board design. That way, you also get a guarantee you have something to solder too in the end.

Again, I don't know what software you use, but it will still make sense to "formalize" even the crudest hack into some kind of footprint/component: your wire bridge could simply consist of two components with one pad each, which share the same net name. That way, you could actually "place" the fix in your board design, and hence, have it documented.

Also, your board might fail design rule checks. Which would obviously be correct.

Create a new minor revision for the intermediate changes and indicate them however you like as long as they can be printed out or copied reliably. They will not be used to create new faulty PCBs hopefully in the future so it is a dead end path.

The next more significant revision should incorporate those changes and any others that may have occurred which will allow new boards to have missing parts placed and traces to be routed correctly. That version does not need to indicate the history of how you got there as it is in the version history already.

Avoid reallocating part designators if you have released any documents outside the design office.

The classic way is to designate a (paper) copy of the schematic as a working master. All changes get entered on the schematic in red. When you're ready to fab the next rev of the board, you hand over the master to whoever is doing the schematics.

At the same time, you need to start keeping a notebook. Sketch out your design ideas as you think of them, and record your design experience. When it comes time to start troubleshooting, record all changes you make in your notebook, as well as marking up the schematics. Then, when you're ready to update the design, cross-check the master schematic with the notebook, and make sure that they agree.