What causes bottom water to rise?
The density of a water parcel evolves as it moves in the ocean. A parcel of bottom water (e.g., Antarctic Bottom Water (AABW) the densest water mass) is much denser than the surrounding water when it is formed near the surface (in the case of the AABW in polynyas and below the ice shelf in the Weddell and Ross Seas). 

As the parcel of AABW sinks, it flows down the Antarctic continental shelf and slope and moves north along the bottom at speeds of 2-8 cm/s. The issue is that the water parcel of AABW will be interacting and mixing with the surrounding water.   

Thus, a parcel of AABW that when it was formed had a temperature of around -0.8°C and a salinity of 34.7, will get mixed with warmer water masses (e.g., Antarctic Intermediate Water, North Atlantic Deep Water) and as it becomes less dense it will be more easily mixed with the surroundings.  

If you have surrounding waters that are more saline and with comparable temperatures, then the less saline water parcel (modified AABW for instance compared to NADW) will rise. The interior circulation of the ocean is predominantly driven by thermohaline processes (differences in density) and the thermal wind equation can be used as a simplification of the dynamics, especially away from the edges (surface, bottom).