Hi John,
Regarding GT's out of bali, I have not attempted GT's based from Bali, I believe there are fish about but there is alot of pressure in these waters due to Population / tourism etc. I have been told January is a good time for bigger fish but ocean/weather conditions may not be optimal.
Some of the operators, including the one Philips mentioned will take you over to lombok where the hunting can be better, but the calmer months are best towards the end of the year.
Another point to consider from Bali are the boat hire prices, you are going to need a decent boat and from these ports and that will mean rather inflated prices.
If you are going to Bali for a holiday and would like to wet a line, give it a try, bring a jigging outfit with heavy jigs too, but if you are on a GT mission there are better grounds to the east.
For further east you may want discuss options with 'Kaiser' one of the sponsors here or look at 'extreme Ulua' as Jon Li suggested, I have used both and was very happy with these charters.
Cheers
Andy