Well, to use a "named file" you'll need a file system. FAT12 is usual on a floppy disk - can just barely get it into 512 bytes (size of a bootsector). Easier to put your file at a known sector (sector 2 - right after the bootsector is simple). Traditionally, an ".asm" extension would indicate source code, but you can name it anything you like. Load it (BIOS int 13h, probably) to some known location in memory and jump to it. Use "call" if there's any reason to "ret" from it.
You're not going to get much of a GUI into 128 bytes. Who made up this "rule"?
If you're new to assembly language, an OS may not be the best place to start.
http://www.osdev.org has a lot of information you'll probably find useful.
Best,
Frank