Now this will be pure speculation since Bitcoin has never been around in a high interest environment and neither are we near a high interest rate but I would think Bitcoin would still continue to rise in value while gold would dip. Gold has always dipped in the past as interest rates rise because people pull their money out of the no return gold investment in favor of the higher interest.
One one hand Bitcoin might be treated the same way because it doesn’t produce any interest (at least not yet) but Bitcoin has extreme speed, especially when compared to precious metals. It takes much more time to transfer precious metals than it does to transfer Bitcoin. Time is money and when interest rates are higher the cost of time increases. Bitcoin’s speed will mean yet another savings in transaction costs.