You almost have the answer in your question; bleed air is hot, compressed air taken from the engine compressors. Bypass bleed air here refers to some of that air which is bled off the engine, but not routed through the air cycle machine (pack). When the air comes out of the pack, its really cold. The pilot has a knob which blends the cold air from the pack with the hot bypass air to adjust the temperature that comes through the actual ductwork; this is similar to the blender box in a car.
For example, in this image taken from this answer on SE Aviation, the bleed air from the engine comes in at the top right corner, and you can see the line for bypass bleed air along the top of the diagram in the pipe labelled "hot air".
