Most bosses don't really like surprises, even pleasant ones. So keep everything calm and proper. Make a formal request in writing for a meeting. Make the tone of your request positive and non-threatening. It's important to avoid turning the encounter into a confrontation hingeing on what your boss thinks of you, yes or no, why or why not.
Say that you've been thinking about your career and wondering about ways you could develop yourself and make a better contribution to the organisation. The best managers are genuinely interested in the career development of their staff, but all good managers should be interested in hearing from people who have ambitions and who can help them solve staffing problems that you may not even know about.
Unless they hear otherwise, managers tend to believe that their staff are happy where they are, and can be pleasantly surprised to find out that people want to do more. So, from the very beginning of the conversation, be confident about what you're doing, but never demanding.