You can get fast internet connection nowadays in Bali especially in Denpasar and Nusa Dua up to 3.5 Megabit per second. (so, that't what they claimed) This is if you have the so-called HSDPA phone to connect to Internet for example the Nokia 6120C.
You can buy the SIM card in Bali if your plan doesnot include international roaming. The easiest way is to get a IM3 SIM card which has Internet connection active already. All you need is just to configure your phone or your modem so it can connect to the service. This one is no sweat since there is a simple manual you can follow. All you need to do is to send sms to a certain number to activate the 3G feature. The price of the data is 1.1 rupiah per kilo Byte, or USD .0001 or so
There are also many many hotspot area that will give you free internet. Restaurants and hotels provide wifi area as part of their service. One of the hotels offering hotspots are: the Westin. Other places includes restaurants; like Bali Bakery at Kuta.
Hmm, I will add more to the list....next time.