Does the new BIOS offer improvements? If not, don't bother.
If you do re-flash, you don't necessarily have to have a floppy. You will need to put the .bin file on a FAT partition though, and boot to another partition in DOS mode if you want to go that route.
I have seen some good flash progs that work within windows, and that may be a better plan for you if they are available for ATI cards..