This is no easy question and I do not claim to know all about it.
Informally, 「[経験]{けいけん}」 and 「[体験]{たいけん}」 are often used interchangeably when referring to a single incident that is a new experience for that person. Regarding whether or not doing so is appropriate, I will leave the judgement to the experts here. All I know for certain is that native speakers just use the two words interchangeably in many informal situations where no one really cares about precise word choices.
When we speak or write more formally about our experiences, however, we seem to become more careful about which word to use.
Formally, 「体験」 refers to any experience that one undergoes in life. If one does not reflect on the experience and learn something valuable from it, it remains a 「体験」. It is a one-time-only thing. However, if you reflect upon your 「体験」 and learn a lesson from it, it can turn into a 「経験」. Your life is that much richer because of it.
In another words,
「体験」 can often happen by sheer chance.
「経験」 often cannot just "happen" without one's active effort following the 「体験」.
Additionally, one could also say that 「経験」 is an accumulation of one's 「体験's」 in the sense that 「経験」 has a longer-lasting effect. If you have a 10-year experience in something, that "experience" should definitely be translated as 「経験」, not as「体験」.