Do not make the same mistake as us.
While we made a big mistake, we believe we have really found the best way to travel cheap to the Gili islands.
When reading the pages with available information, we found that the cheapest option to make the trip was doing it on your own, taking the 4-hour ferry from Padang Bay to Lombok Island, then to take a bus to Bangsal, and then take another boat to some of the Gili islands. That was what we did, and it was a terrible mistake. First, because it is very difficult to save with this option, although we got a somewhat lower price, it was practically by luck.
The trip took almost 11 hours in total, and it was terribly stressful. The 4-hour ferry seems endless, then when arriving in Lombok, there were no buses available to get to Bangsal, so we had to beg a taxi driver (who luckily agreed) to take us to Mataram. And from there, take another taxi to Bangsal, which also luckily agreed to take us for a reasonable price. If you do this whole trip, with the established prices, they will be more expensive than taking the speedboat from Padang Bai.
Worst of all, unless you intend to tour around Lombok, and go to a place that you know is beautiful, what you will see on the way, it is not really beautiful.
The real best option
If what you want is to save, take a bus, the cheapest you get from Ubud to the port of Padang Bai, and when you get there, there will be many boats available, that you will probably get a much lower price than you can get from the agencies in Ubud. When you find it, try to negotiate the round trip price, and go by speedboat. Believe us, that is the best option.