From the HP website I got a compressed file called sp30515.exe. The file is self-decompressing when it is run, but in this case I couldn't simply extract the files using a compression tool.
I used wine to extract the files like this:
$ wine sp30515.exe
Once the files was extracted I found the image file containing the actual BIOS upgrade. The file was named rom.img
Now all I had to do was to write the image file unto a floppy disk, and this can easily be achieved in any Linux or BSD using the dd command:
$ dd if=rom.img of=/dev/fd0
And that was it.