Most areas of Bali have OK mobile phone coverage if what you want is just phone calls and text messages. But to get a reasonable Internet service from your mobile phone company you need the so-called 3G service (3rd generation) for reasonable data speeds. This means the equipment installed at the cell tower you are connecting to needs to be up-to-date.
In Bali, areas where mobile phone usage is growing rapidly (i.e. the cities and tourist centres) the equipment is frequently updated to cope with demand, and these updates bring 3G services. But away from these growth centres you may be out of luck.
As an example, I was recently in Lombok, and in Kuta (a small place in the south) Telkomsel had no 3G services, while one of the other operators did (XL I think). But in Mataram/Senggigi (more of a growth area) Telkomsel services were excellent.