When we did it years ago we came from the other direction and hired a boat from Flores.
From Bali if you do it independently, it's going to be complicated; you have to island hop across Lombok and Sumbawa before trying to find a boat.
There are tours from Bali you might try:
http://www.balikomodotours.com over 5 years ago
I also found this which suggests flying from Bali to Flores:
"There are daily flights from Bali to Labuanbajo (the base for trips to Komodo) with AIT and Transnusa - any travel agent in Bali will be able to book these for you, or you could go directly to the offices of these airlines when you arrive at the airport in Bali (they are outside the domestic terminal, a hundred yards to the right when you emerge from International Arrivals.
There are plenty of hotels and guesthouses in Labuanbajo, which is a pleasant little port with good views, and lots of dive opperators that double as travel agents - they or your hotel would be able to arrange your tour for you (there are also some hotels on the offshore islands).
Boat trips of varying degrees of comfort (and price) run to Komodo and Rinca and various snorkling spots/beaches, and are definitely worthwhile. A simple day trip from Labuanbajo to Rinca will let you see dragons and other wildlife, and give you a chance for a bit of snorkling; an overnight trip will get you to Komodo and Rinca (very similar though having been there twice I'd say there's no need to go to both if all you want is to see the dragons - Rinca has them and is a bit nicer) and will offer some better snorkling." over 5 years ago