Democracy has to do with politics, capitalism has to do with economics. The fact that GWBush chooses to use the word “democracy” instead of capitalism does not change the meaning of the words. It’s just an extra proof that he’s plain stupid.
Yes, you could have capitalism without democracy (such as in dictatorship situations), but usually money gives political power, so unless the big wallets are part of the system, it can be very dangerous to make too much money in such a situation. The opposite is even more rare and can only work in very small countries, since democracy (ie freedom of speech and political will) is usually irrelevant when people cannot control the means of production. It has been tested, and failed.
In theory, both systems could work, and there are also intermediate positions that have been fairly successful at times (such as Scandinavian Eurosocialism). It doesn’t have to be an “all or nothing” situation. You could have a country with fairly high taxes that would help the less fortunate members of society, or strict censorship but still some basic rights of freedom (think of the 50s in America for example – I’m not saying it was perfect, but it was not the same as the USSR).