Assuming the RAM is of the same technology (GDDR3 vs GDDR3, GDDR5 vs GDDR5, etc.) and running at the same frequency; doubling the Bus Width will directly double the available memory bandwidth.
Purchasing a GPU based solely on the Bus Width and amount of RAM is probably not the your best option though.
If you could list the exact cards you are looking at, their intended usage and your budget we could help you find your best option.
It would also be helpful if you could post your system specifications including detailed information on your PSU and your monitor resolution.
128 bit and 256 bit are referring to the width of the GPU's Memory Bus.
It is one of three items that define the Memory Bandwidth, the other two being the type of RAM and the speed of the RAM.
Just because a GPU has a wider memory bus does not mean however that it has more memory bandwidth.
As an example, the GTX 260 has a 448 bit memory bus and 111.9GB/s bandwidth where the 4890 has a 256 bit memory bus and 115.2GB/s bandwidth.
This is because the 4890 uses GDDR5 RAM as compared to GDDR3 on the GTX 260.
As for your second question, I would recommend an ATI 6870 for around $230.
It will give you plenty of performance and is priced to move.