There are buses from Santa Cruz to San Matias in Eastern Bolivia, on the border to Brazil. It takes around 15-18 hours on dirt roads. Once in Mato Grosso (on your way to Cáceres) the roads are very good and modern.
You won't easily find information on buses online, just go to the bus terminal once you're there in Santa Cruz and buy your ticket. Don't plan too tight as there are often very few buses per day between destinations in Bolivia, sometimes not even every day. It might also be at 6 am or similarly unlikely times.
Get your passport stamped in San Matias (exit stamp Bolivia) and in Cáceres (entry stamp Brazil), even though it's 100 km from the border. Note that the border office in San Matias isn't always open. On weekends, the official opening hours are 7:30 to 14:30 (as of November 2014). In Brazil it's 24h at the federal police.
You are not allowed to bring certain plant and animal products into Brazil, so try to finish your food before crossing the border. I wasn't checked, but it could happen and I suppose it's better to avoid trouble.
You have to take a taxi from San Matias to the border which should be no more than 7 Reals (if shared) or 15 Reals (single) (prices as of November 2014). Of course you could also pay in Bolivianos if you still have some. But you will need Reals to pay the bus from the border to Cáceres, a single ticket is 19 Reals, so exchange some money while in San Matias. There is an exchange office in town. You can also take a shared taxi, which should be 25 Reals and is much faster and more convenient as it can bring you directly to your destination in Cáceres, rather than the bus terminal. In my case, it brought me to the federal police for immigration first, waited for me, then we went to the bus terminal for onward travel at no additional cost. (Although not every taxi driver may be as nice and friendly.)
Good luck to anyone on that route!