Hi, Laura,
I think this is what you want to do, only over your desk instead of a doorway, yes?
ikea hacker: book case bridges over doorways
According to the OP, they took Billy cross pieces from other height extension kits to make the bottoms. If you want to do more than a couple height extensions' worth of floating sections, I would imagine that you could get used Billy shelves or cross pieces from Craig's List or the Ikea As-Is section so that you do not have to buy so many extra height extensions and have so many pieces left over.
Hope this helps! You may also want to look at my Billy height extension post in the Ikea Hacker section for height extension specs and ideas.
Otherwise, one or more Lack shelving units, which may be wall-mounted, could also be a fine bridging piece:
IKEA | Storage furniture | Bookcases | LACK | Shelving unit
Here is a wall-mounted Lack flanked by Billies. In this case it was used to frame out a TV stand to make an entertainment wall, but you can use the same principle to frame out your desk:
ikea hacker: projection tv entertainment center
***addendum: Unless you have a particular desk you like and specifically want to incorporate into your design, you could alternately do wall-to-wall Billy bookshelves, get a tabletop and two legs and affix them to a fixed middle Billy shelf a la the Expedit desk:
IKEA | Tables & desks | Desks | EXPEDIT | Desk
such that the Billy bookcase acts as the other two legs of the desk. Also, I would use some kind of mounting brackets from underneath to secure the desktop to the shelf. A bonus to this configuration is that you now have built-in storage space underneath your desk as well!
Since you're handy enough to be contemplating mounting height extensions to the wall, you might even be able to figure out how to modify an Expedit desk to attach to a Billy, or create a drop-down desk surface using a tabletop on hinges.