9 Days in Bolivia

If you're doing it with an organised tour then it's realistic. Reasonable? It's a matter of individual taste.
You have four places and nine days. Imo, it's too packed and too rushed.
Normally, you need time to acclimatise in La Paz, three days as a rule of thumb. For Salar de Uyuni you need three full days plus travel time (overnight bus from La Paz is optimal). And, the remaining one-two days can be used for visiting either Lake Titikaka, or Sucre, or Potosi.

You might consider flying La Paz-Uyuni-La Paz and La Paz-Rurrenabaque-La Paz. Amaszonas has connecting flights via La Paz between Rurre and Uyuni and vive-versa.
But take note of #1's comment on acclimatisation, particularly if you have no previous experience at 12000 feet.

Agreed. No way can you fly into La Paz spend half a day there and move on by flying to Uyuni. The altitude will get you if you do not take time to acclimatize. Uyuni is extremely high, and once you get on a jeep to go out onto the salt flats, there are virtually no medical facilities if you get into trouble.

You could fly into La Paz, then spend a couple of days going up to Copacabana to go out to Isla del Sol on Lake Titicaca, then go back to La Paz. Then you should be well enough acclimatized to fly into Uyuni.

With 9 days only, I think you'd either need to drop the plan for the Amazon (Rurrenbaque) or don't go up to Titicaca.

Thank you all for your responses so far. One thing I forgot to mention is my wife and I will have spent the week prior to this in Cusco and Machu Picchu, so we should be reasonably acclimatized for La Paz. It won't be like coming from sea level. Also, where we live now is 4,000 feet above sea level, so we are already partially there. However, it sounds like we should scale back a bit to appreciate things more :-)

So, if you had to pick three things to see in nine days in Bolivia, what would they be? Salar is a given for us, and I think Lake Titicaca (which I am thinking two days with an overnight stay). What else would you highly recommend in terms of history, interest, and beauty?

So, 9 days, no acclimatization needed. Even if you fly, including transport you're going to need 4 days for Uyuni and the standard jeep tour there. Add in 2 days for La Paz, coming and going from Uyuni, and that only leaves you with the 3 days you'd need to go to lake Titicaca, including transport time there and back.

Of course you could do the 1 day version of the Salt flats tour from Uyuni, but there's still no way that gives you time to go to the Amazon in 9 days. Maybe it would give you time to stop in Sucre, if you go overland between Uyuni and La Paz. Sucre is a lovely small city.

So if we arrived in the morning, is it possible to simply fly to Uyuni right away and start the tour? Our flight arrives in La Paz around 9:20 AM. That would be part of the four days, or would it be five days? We could fly down, take a bus or car back and stop in Sucre for part of the day before hitting La Paz that evening?

Just trying to get a feel for what is reasonable :-) Thank you very much for your advice - please keep it coming!

I'm all in favour of tourists visiting Sucre, but Sucre is not (definitely not) on the way from Uyuni to La Paz. You would have a 3-hour drive to Potosi, then another 2-3 hours to Sucre. The >700 kms from Sucre back to La Paz - through Potosi again and then Oruro - takes me 8-9 hours in a biggish vehicle, allowing for pit stops. By 'bus, it's all night. On top of that you risk a delay somewhere along the road.
BoA does have direct flights from Sucre to La Paz, but even so you would really be pushing your luck.

The jeep tours leave Uyuni around 10am in the morning, so arriving La Paz in the morning, you'd need to wait until the next day to start one of the 3 day tours in Uyuni.