I have the flywheel diameter, weight etc of the exercise bike therefore a way to calculate the velocity and power and time taken?
I think you are missing the most important aspect of an exercise bike which is the resistance to the flywheeel rotation at a constant speed. There is always some sort of resistance to constant pedaling. Sometimes it is as friction band on the outside of the flywheel, sometimes it s felt pads rubbing on the flywheel, sometimes it a fluid turbine or fan, sometimes its magnetic or electromagnetic resistance.
If you don't know the the resistance you can't calculate power other than the accelerations.
I have made a watt meter for a fluid resistance trainer measuring the rpm of the flywheel, but I had a curve of power as a function of rpm supplied by the manufacturer.