Your ping isnt always dependable on your bandwidth, even though a higher bandwidth would usually have a lower ping. It also depends on your location in relation to the game servers location and also like you said if there are any other programs using your connection. Just before you are about to run your game use task manager and click on Networking. Your network utilization should be very low, if not then you have other programs using your bandwidth. I would check your processes and applications tab to see if you can end some programs that are using it up. BUT BECAREFUL NOT TO CLOSE TO MANY OR CLOSE ONES THAT ARE USED BY THE SYSTEM.
Hope this helps