ping is the amount of time for a chunk of data to go from your comp, to the server and back, you can increase your bandwidth to 1000000mb/s but your ping will stay the same.
the bandwidth amount will reduce the lag during intense data transfer, such as downloads, lots of players in a game of UT3, or even just browsing the web. it will not however reduce the slight latency you get in a game.
you can change the service provider, or the type of service (cable/dsl/fiber optic/etc) to change the ping (need to do research to find out which one is the fastest in your area)
but even then, your ping is half based on who is hosting the game/download/website. so the change may not even be noticeable.