As I see this question is not getting any answer yet and as I have traveled several months in Indonesia, I will attempt an answer.
Starting from Sumatra
It's possible to cross the whole island by motorbike, as one can read on many forums & guidebooks, public buses & tourist buses do travel from city to city in the island. And there is not one point "where the road ends" (unless it reaches the sea!). Sumatra is huge however (and has a lot to offer), so plan several weeks to cross Sumatra unless you rush through. Roads can be a bit bumpy, nothing unusual for southeast Asia though.
One might want to use Medan as a starting point in Sumatra. The main reason being that it is already a "base" for many locals & foreigners traveling through the huge island.
Buying a motorbike:
Medan has a significant size, hence will probably have several motorbike shops where you can buy the motorbike of your dream for this epic adventure.
Otherwise if you want to bring your motorbike from Malaysia or Singapore, it is possible. See how some ferries go from Singapore to Sumatra
Going first to north: probably going through Ketambe & then to Banda Aceh, note that the Aceh province applies the Sharia law.
Then one would come back to Medan (as I think there is no other road to go back south).
Finally, head south (stopping by Lake Toba, Pulau Banyak & more), until Bakahueni. From Bakahueni, take the ferry to Java.
As for Sumatra, it's possible to cross the whole of Java by motorbike, as one can read on many forums & guidebooks, public buses & tourist buses do travel from city to city in the island. Java is also huge (one may argue it has more than Sumatra to offer), so plan several weeks to cross Java unless you rush through. Roads can be a bit bumpy, nothing unusual for southeast Asia though. In my opinion, Java is more developed than Sumatra, so roads "should" be better.
You can take the ferry from Banyuwangi (Ketapang) to Bali. I've done this, it's super quick & there are many ferries.
The easy part. Bali's road are a blessing after the rough roads of Sumatra & Java. Bali has some very touristy parts (like the ugly-crowded-overpriced Kuta), but it also has very rural areas that you probably want to explore. Being in southern Bali might be a good connection back to civilization though, & some areas are less touristy.
Take the ferry from Padang Bai to Lombok (Lembar). I've done this too, it takes around 4h & it's around 40'000 IDR per person.
Lombok as great roads for some reason. You can litterally cross the island in less than 2h. But you might want to take your time by going south and relax, or north to try to do the horrible 3 days Rejani trek (you walk for 13h on the 2nd day).
Sumbawa is huge & mostly under-developed, think "Sumatra style". Many vehicles cross the whole of Sumbawa from west to east in about 14h (non-stop), roads are pretty good from my experience of crossing west to east. But I suspect that going out of that road could lead to many surprises, it'd be a great adventure though.
Take the ferry from Sape (Sumbawa) to Labuan Bajo (Flores).
Flores is huge & mostly under-developed (yes, again!), think "Sumatra style". So plan plenty of time, several weeks, if you want to explore it without rushing. There is already a question regarding riding a motorbike through Flores.
One might want to then carry on & go to Timore or Sulawesi. Which sounds reasonable :)
Some ferries do leave from Flores (Labuan Bajo) for Sulawesi every 2 weeks, enquire at the official desk in the port to know further (or call some diving schools in Labuan Bajo, they might be able to help).