Use subst command to mount some directory to A:

Syntax:
SUBST [drive1: [drive2:]path]

This would make contents of c:\floppy visible in a:
SUBST a: c:\floppy

But I'm not sure why would BIOS update wanted A: in the first place, does it use some batch file? Usually you can do BIOS update from HDD just fine and it's better because floppies can be flaky.

perhaps the update is supplied as a program that installs the bios update to a floppy ive had a few of these

It seems that the update needs to be in A:. If it is run from any other place, it copies the update to A: then installs it.

I thought about using SUBST, but I was wondering if it exists a proper virtual floppy emulator (one that at least could patch INT 13).

Flopper is used to start up bootable disk images from DOS. I'm not sure how well it would work with what you're referring to.

The other thing that comes to mind is certain Linux bootloaders, but it's been too long since I've looked at them. I think it was SystemRescueCD – or was it Ultimate Boot CD? – that includes a bunch of bootable floppy images (including one for DOS) which you can select from the boot menu; you can even substitute your own if you don't want to reconfigure the menu. I think they all use Syslinux to accomplish this.

If you are using a real DOS PC, why not just make a physical floppy from the image and use that?

His floppy drive is broken

Are you sure it needs the A drive? Most BIOS updates use boot disks so that it can ensure that there is nothing in the background that could interfere with the update (TSR's and such.) If it's a DOS machine, you can arrange this by hitting F8 during the boot (to turn on line by line confirmation of CONFIG.SYS & AUTOEXEC.BAT,) then just hitting N (No) for everything. Put the flash software and the binary in the root directory of C, then just run it from there. Some come with an AUTOEXEC.BAT file that also runs the flash software (with the correct options & the name of the binary,) automatically. Just use the command in that file.

All that being said, I am not personally aware of the details for every single BIOS and flash program available. Yours could be different.

You can use SYSLINUX to boot up a floppy image as A: Google for "SYSLINUX" for more information. I recommend using the last release in 3.xx version, ie. SYSLINUX 3.86. It is completely free and open-sourced.