Whoever it is that has 55°C water temp, I thought it had to be 60°C min to avoid legionella?
OP it's insane that 65°C is the hottest your boiler goes. The engineer left mine in the wrong settings after servicing and it was 95°C. When the really cold spell hit recently my 60°C bath felt too cold within 15min of being in it without having added any cold water and I had to temporarily turn the boilers water temperature up a bit for a few weeks. I think the bath itself was cold and stealing the heat from the water, so you could try heating the bathroom before running the bath.
Those wanting constant hot water, there's a setting for that on my boiler, means it keeps a small amount of water hot and ready to use so no cold comes out the hot tap for handwashing etc. But means the boiler is on more than it would otherwise be so will presumably cost more.
If you want to top up the bath while you're in it it's easy, so long as you've got two feet and the right taps. Pull the plug at the same time as turning on the hot tap so the initial cold water goes straight out, putting the plug back in again when the water starts coming through hot. Use your feet to do it and you don't even have to sit up. If you're losing too much water hover the plug over the plughole to slow the flow rate. You'll need one foot on either end of the plug's chain to do that.
Not sure what combi boiler I've got but by the time I've gathered my pyjamas, chosen my clothes for tomorrow, used the toilet and found a book to read, the bath is ready. About 10min I'd guess? Then add cold water as appropriate and get in. I can also do the washing up and run a bath at the same time although the water pressure is crap when it's coming out of two taps at once. It's not a problem though, if it came out faster the bath might over run before I'd finished the washing up. I wash up under a running tap.
OP if your radiator is too cold have you turned up the thermostat on the radiator to the max? Mine goes up to 5, on 2 it won't feel particularly hot.