The real interesting question is what is actually happening when the price of bitcoin skyrockets: Let's use a wild example and say bitcoin went to $100,000. This would be inflating the general money supply assuming people were buying things directly with bitcoin. You are placing in a dollar substitute, kind of like counterfeiting (not the greatest term, but best example I could think of). The overall effect is more money in the system.
Since nobody is buying things with bitcoin directly, it remains a derivative of the USD like almost all other fiat currencies. This also makes bitcoin constrained by things like dollar liquidity shortages, etc, where federal reserve monetary policy is essentially bitcoin monetary policy.