I don't think this is possible with an ISO image - you can't "write" to a disc image. That's not what the format is for. There is no such thing as a CD drive which can directly write files to a CD.
You can, however, use a tool like MagicISO or PowerISO to remove or add files to an existing ISO disc image. That being said, when you actually save the ISO image, it ends up re-writing the entire disc image due to the way the format is.
Finally, if the underlying filesystem in the ISO file is UDF-based, it may be possible to implement writing directly to the virtual drive by letting it act as a virtual CD-RW. That being said, I believe the performance hit would be a lot worse then just using an ISO editing tool.
If you want to simulate an actual flash drive, what you're looking for is a virtual filesystem. One of the easiest ways would be to use TrueCrypt to create a virtual (encrypted) filesystem in a single file. You can then mount that file and use it like any other hard drive/flash drive. Unmount it, and your data is stored in a single file (which you can re-mount whenever you'd like, on any computer system).
There are alternative programs which can do the same thing (and without the encryption), but TrueCrypt is free, open source, cross platform, and pretty easy to use.
That being said, since you commented on what you really are trying to accomplish, you should use a virtual floppy disc emulator. This will allow both read/write access to the virtual drive, and should work with the appropriate drive letter.