There is no relationship between the quantity of VRAM and the width of the bus.
You need more VRAM to store higher quality textures, store larger frame buffers for higher resolutions and to support higher levels of anti-aliasing.
The width of the bus is about how quickly you can get data in and out of VRAM, but this also depends on the clock speed of the memory and the compression being used. Nvidia and AMD have both moved to narrower bus width with faster memory and better compression because it reduces manufacturing cost and power usage while maintaining performance. It is also likely when they move to 20nm or 16nm processnodes that it will no longer be possible to connect a memory bus with more than 256 bits.
In short, the...