Demand-pull inflation is not happening with Bitcoin. Again, inflation refers to the devaluation of currency. If the purchasing power of Bitcoin goes up, Bitcoin is deflating, not inflating.

Maybe you are trying to say that the USD is inflating (w/ demand-pull inflation) because USD is becoming less valuable, relative to Bitcoin.

But that theory is still problematic, since you can't measure inflation against just one asset. An asset might appreciate because of a shift in consumer demand -- the currency itself might not have "devalued." Instead, a better way to measure inflation is wrt. a basket of goods, like CPI. CPI has not changed much in the last year, which implies that the USD is not inflating much.