You've hit up against the classic weakness of a control system that uses the temperature of a single room (the hall in your case) to control the temperature of all the rooms in the house! It can never work properly, yet it is the most common heating system in the UK!
I'm assuming that the bedroom rad is working and gets nice and hot -- it's simply not able to pump out enough heat before the thermostat in the hall switches all rads off.
One simple 'cure' would be, as you suggest, to fit a bigger rad. How much bigger depends on the room size and other factors. A central heating engineer or knowledgeable plumber can do the calculation for you, and there are websites to help. You would be advised to get the all the rad outputs 'balanced' as well.
Another, better, cure is to fit thermostatic radiator valves to all rads, and then turn the wall thermostat up to maximum (effectively turning it into a permanently-on switch). The pump would then run all the time the heating was 'on' -- which does it no harm -- and the temperature in each room would be individually controlled by its TRVs. But you would still need to have big enough rads in each room, especially the freezing bedroom.
(If your system has no bypass across the pump you will need to leave one of the rads without a TRV, so that the situation where all rads are shut off with the pump running can never arise.)
Hope this helps.
Big Al
