Not sure of the exact meaning within this context, but Bye is a word often used in mining often in terms of direction ie. Inbye, Going in away from the shaft. Outbye, the reverse. Backbye meaning that part of the colliery behind the working districts (same can be said of outbye). It was common in East Cumberland, West Northumberland around that time to sink shafts in pairs. The one to the dip would be the engine shaft used to draw water, whilst the rise side shaft would wind men and materials. In this local during this period winding was via horse gin whilst pumping was via bob gin. I have never queeried how winding for access to the pumps was carried out, perhapse the answer lays within your queery Clive