Bitcoin fans keep saying "prove it is a bubble" because they do not believe it is - but this is a false question.

The real question all you bitcoin fans should be able to answer is: Prove that bitcoin is not a bubble.

A bubble is when the price of something is far higher than the fundamental value.

Bitcoin gives you ownership of nothing (a stock gives you ownership of tangible assets)
Bitcoin pays no dividend
Bitcoin gives you no right to future payments (bonds give you the right to payments)
Bitcoin gives you no patents or trademarks
Bitcoin gives you no legal rights

Given these facts, you Bitcoin fans need to prove that the fundamental value is different from zero (or close to zero) - otherwise it is a by definition a bubble