What if I set the setting to ZERO (0)?
Would this be bad then?
You can't set the Proportional bandwidth to zero; 1.5deg is the lowest.
Let's assume that you could set it to zero. The boiler would run at full tilt until the stat read 19°C and then switch off. But the radiators would carry on giving out heat as they cooled down, so the temperature would rise above 19°C to say 20/21°C. The room would then start to cool down until it reached the stat turn on of 18°C and the cycle would start again. You then have a temperature swing of 2 or 3 degrees. The proportional bandwidth "slows the boiler down" as it approaches the desired temp to minimise the overshoot.
You don't say what type of boiler you have, but there are boilers and programmers now available which work together to control the gas flow according to requirements. Most of these systems are proprietory as there is no agreed standard for communicating between boiler and programmer. The OpenTherm standard is used by some manufacturers, but it does not have any official backing.
Back to your "problem"
According to the CM907 spec the temperature control accuracy is ±0.5°C, which is considerably better than mechanical thermostats with anticipators, where you could get temperature swings of several degrees, which is noticeable. The display only changes in 0.5°C steps, so the fact that you have it set to 19°C and it says actual is 18.5°C means that the actual is some where between 18°C and 19°C.
The thermostat is in a bedroom as it runs the heating for the bedrooms.
This is unusual, to say the least! Is there any particular reason for this such as someone bed-ridden etc or is it how you found it when you moved in?
What controls the temp for the rest of the house? Do you have TRVs on all the other rads?
Provided the regular on and off of the boiler does not disturb you, I would ignore it. The programmer is doing "what it says on the tin". But, as I said, there is no harm in experimenting with the Proportional Bandwidth. Set it to the max of 3°C and see what happens. The real criteria is how much the temperature fluctuates about the set point.