A typical bath can be about a 100 litres. A typical header tank system with stored hot water and 22mm pipes to the bath can fill it at 20-30 litres a minute. i.e between 3 and 5 mins.
With sufficient pressure a 15mm pipe could easily deliver 15-20 litres a minute but as your combi is probably only capable of producing about 12 litres of hot water a minute, then that is the limiting factor and is why it will take so long to fill your bath.
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