I don't quite understand the bypass air
Cold air accelerated backwards provides forward thrust by reaction. What really matters is the amount of mass accelerated backwards. Its temperature is not important...  

Concerning the 'percent of air sucked', it depends on the design. A pure turbojet doesn't produce 'bypass air', and a turbofan may reach a ratio of 10:1, that ratio being the relation between the mass of 'cold' air pushed backwards by the fan in a given time and the mass of air that passes through the combustion chamber...