Over most of the engine length, the bypass air travels at the same speed but is much faster than the core air entering the combustor
Let's assume a typical fan engine like the CFM56 pictured below. It starts with an intake which helps to equal flow speed regardless of aircraft speed. The first stage is common for both the core and the bypass stream and increases air pressure without accelerating the air. Next, the flow is split into the core and the bypass stream. The core stream is compressed further and again the pressure rises while speed stays roughly constant. Before entering the combustor, the air is slowed down substantially so combustion is actually possible within the engine.
Cutaway view of a CFM56 fan engine (picture source)
In contrast to that, the bypass stream continues at roughly the speed at which it entered the fan. This is illustrated by the constant cross section of the bypass duct in the picture above. Only at its end does the duct narrow in order to convert the air pressure into speed. Doing this any earlier would mean higher friction losses.
In contrast to that, the core air is slowed down in the diffusor and picks up speed again as it is heated in the combustor. With the higher speed of sound of the heated air, it now becomes faster than the bypass air as it travels through the turbine stages. In the nozzle it is accelerated again in order to convert the remaining pressure into speed.
Therefore, the gas stream leaving the engine core is much faster than the bypass stream, but has gone through a deceleration and then an acceleration while the bypass stream never got decelerated.