100' of 3/4" PEX pipe holds about 1.8 gallons of water. You would have to run a bathroom sink almost 2 minutes before it would start to get warm.
A small electric tank heater VERY near (In) the bathroom would provide nearly instant hot water to the sink for washing your hands or shaving. The link is to a 6 gal unit.
These small units are slow to recover, so you want enough storage to take care of hand washing, etc. At 6 gallons it will also have enough storage to buffer the initial almost 2 gallons of cold water in the pipe when you are taking a shower until the hot water from the main unit takes over.
Electric resistance is the most expensive way to heat water. However, a small point of use heater in series with a gas tankless or electric hybrid would save both energy and water when the main heater is far from the master bath.
Copper pipe has a slightly larger inside diameter than PEX. That same 100' of 3/4" pipe in copper would store about 2.5 gallons of water instead of 1.8 for PEX. In addition to the water in the pipe, the thermal mass of pipe has to warm up, and then if it's not insulated and in a slab (not code) the copper is going to conduct the heat more readily to the concrete than PEX. For those reasons I'd say copper will take longer to get hot water than PEX.
I want to again say that the best solution is not to have a water heater 100 feet from where the water is being used. Be sure to insulate the hot water line in the slab to R5 - not the R3 pipe insulation you find at the hardware store.
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Great solution for hot water in bathroom from garage
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