If you're going to try this yourself, make sure you understand everything really well before you start. Don't even think of touching any tools until you know all about the physics of the string. I've seen far too many instruments where someone has done a really decent job of the woodwork without realizing that the bridge has to be in a specific location (which is an inch past the end of the bass). I already had a very in depth understanding, and still spent a huge amount of time reading up on the internet. If you don't know it all inside and out, you should probably get a book.
For the actual drawing, I used a free 3d modeling program called Blender. It's not a true cad program, but I know how to use it reasonably well, so it worked for me. Also, I run linux, and it's available there.
First I drew a scale 3d drawing of all the parts. Neck, body blank, pots switches pickups bridges, everything. I also drew some placeholder objects to help me with some other stuff like scale length. Since I had everything to scale i could mess around with the layout at will without any fear of unintentionally overlapping any parts. I drew the body such that it fit within the bounds of the blank with all the other components in place.
As far as shape goes I wanted something of my own design, but I figured there's no shame in getting started off in the right direction. I picked a bass that I liked the look of (in general), traced it with bezier curves, and then tweaked the heck out of it until it looked right to me and made visual sense with the rest of the design. I made the body very long, because the neck is quite heavy and sticks out a few inches further than on most basses. I even angled it on the blank to squeeze out a couple extra inches. The end result has only a vague resemblance to the outline I started with, but I'd still recommend this method, since it makes it a lot easier to get the overall proportions right.
At this point I also figured out my bridge spacing. I had spaced the nut for equal spaces. The fanned frets don't allow you the luxury of arbitrarily spacing both ends of the string. I got stuck trying to wrap my head around the geometry for a while, Had a couple discussions on talkbass about it, in which most people gave me the wrong advice (Told me it wouldn't matter). A couple people did understand the geometry though, and were quite helpful (Thanks to Pilotjones in particular). The gist of it is that any movement away from equal centres at the nut needs a proportional (not equal) movement at the bridge. If you look carefully in the later pages you can see that my treble bridges are closer than the bass ones.