I tried using the obvious "Create Image file from files/folders" option. However, when I selected the .bin and .cue file and hit the "build" button, the resulting ISO didn't behave like a disk at all. When I mounted it, it just appeared like a folder. Inside were just the old .bin and .cue files.
This is supposed to be for some software, so when I mount it I should either be able to see all the files inside (like the installer/executable/etc) or it should automatically open up some kind of installer.
There is the possibility that the .bin and .cue files were screwed up somehow, it's easily over 2 decades old.
EDIT: Solution. I used Virtual CloneDrive (free software) to open the .bin file. Worked fantastic! Just like mounting a normal ISO file.