You have a combi boiler, I gather.
A combi boiler can heat X amount of water by Y degrees, in a minute,
If your bath tap delivers 2X amount of water, it will only be warmed by half a Y. In winter the incoming water will be very cold and needs to be warmed by more degrees.
It is usual for bath taps and their pipes to be bigger than sink taps, so will deliver more litres of water per minute than sink taps, so, from a combi, the bathtap will be cooler than the sink tap.
Your method of turning on the cold tap will reduce the amount of flow available, so the bath tap will be hotter.
I expect that if you turn down the flow on the bathtap, the water will come out hotter and slower.
Sadly this is normal for ordinary combis.
There might or might not be some other problem. If you run the bathtap into a bucket, time it to full, and calculate how many litres per minute it delivers, that will give a big clue, but the power of the boiler, and the temperature of the cold and hot water will give more.