One of the key skills that a bachelor's degree in math will teach you is the ability to be extremely logical. This is important in almost every career and in everyday life. High-level mathematics is mostly about proving or disproving equations by logically analyzing them to their simplest levels. This capacity for logical analysis is useful in careers in finance, statistics and other careers where a large amount of data is generated and a logical mind is necessary to derive its meaning.
Another component of high-level mathematics is forming a problem. University-level mathematicians don't just solve problems. Rather, they take other problems or real-life situations that seem unsolvable and frame them in such a way that the logical skills mentioned above can be applied to reach a solution.
This is arguably more important than the problem solving itself. After all, all the problem-solving skills in the world are essentially for naught if you can't frame problems, and mathematicians leave their courses with the ability to do so.
People with bachelor's degrees in mathematics have a number of career options available to them. Financial analysts often have math degrees due to the information they have to process. The same goes for actuaries, statisticians and cryptographers, who work with banks and other companies with sensitive information to protect it using advanced codes.
Programming also demands high-level math skills due to the fact that programs need to work every time. In order to test this, a programmer needs to go through his entire piece of work, testing situations from every angle. The ability to logically deduct where problems could come up and determine which angles to test from is invaluable, and math degrees often teach this ability.
Math degrees are difficult and rare, but they also teach a variety of skills that are important to a variety of employers. This means one thing: money. Securing your employers' money through cryptography, helping him make decisions through financial analysis, and writing a program that makes his processes several times more efficient are all high-value jobs and are therefore compensated extremely well. According to a 2009 Wall Street Journal study mathematicians had a median income of almost $95,000, which means there are a substantial number of math graduates making higher salaries.