I attempted to visit the SW corner of Bolivia twice last summer but was forced to turn back with bike trouble both times. I'll be back for another attempt in the spring of 2011.
Anyway, my second attempt was from Uyuni and I rode SW as far as the unusual 'Valle de Rocas' which is SW of Culpina K. It should only take you a few hours to ride there from Uyuni but it will give you an idea of the road ahead. If you're happy with the amount of sand you encounter then continue, if not turn around. If you have camping kit with you I highly recommend a night at Valle de Rocas. As you head south you will see a track that forks to the right and leads towards the Mars like landscape.
You can top up with fuel in Can Cristobel before riding to Culpina K. If you're not sure which way to ride just wait for a 4x4 to pass by and ask. Alternatively, send me an email firstname.lastname@example.org
and I'll try to send you my GPS track.
My expectations of the road were that it deteriorate and become more sandy, however I was told that the worst section for sand is on the direct route Nth/Sth from the border to the Salar whereas you'll be approaching from the NW.
If you decide not to go this way, no problem. NW Argentina is stunning. The road from Uyuni south to the border is dirt all the way and intersects with the road from Potosi to the border (which is the way I entered Bolivia). It was great riding much of the way with the road often running in dried riverbeds. I can't remember how much of the best bits were Nth or Sth of the Uyuni junction though. The road is being improved further south so there are a lot of detours (at least there were last July).
If you follow Ruta 9 into Argentina then the 49km in/out ride to Iruja (all good dirt) is spectacular.
From Argentina to San Pedro de Atacama you have two options. The paved Paso de Jama or the dirt Paso Sico. I plumbed for Paso Sico and it was STUNNING. Took so many photos along the way I ended up camping at 4200m in -10C. The road passes close to the famous Polvorilla viaduct on the Tren de las Nuebes. You can get fuel in San Antonio de Los Cobres and there's a Hosteling International affiliated hostel at the far end of town towards the railway bridge and the road to Paso Sico.
From there though it's a long way to San Pedro with no fuel. It's dirt all the way but will be no problem on your WeeStrom even with road tyres.
Most of this is covered in Chapter 19 on my website - http://shortwayround.co.uk
Whichever route you take it won't be the wrong one - the whole region is stunning.