I think you failed to assume something here. First, the assumption here is that by the time we have bitcoin notes and coins (physical coins like dimes, quarters, etc), there has been great adoption of the Bitcoin already. If there has not yet been a great adoption then you would not likely be paying bitcoins at a restaurant. Second, if there has been great adoption, then the prices for sure has stabilized already or, (pushing our luck here) there is no other currency already but bitcoin itself.
If you assume that there are no other currency but bitcoin, then you don't even have to convert your money into dollars. But if there are still other currency beside bitcoin, like the USD, then you can convert it similar to having Yen, Euro, Dong, Etc. The prices doesn't fluctuate that much hence solving the problem.
Who says that after a great adoption the price of bitcoin would get stabilized? Are you assuming that the great adoption will change the way bitcoin works? Or the world will make a new version of bitcoin which would be controlled and the people will decide if it will be stable or keep fluctuating?