It’s fair to say that transport in Indonesia can be problematic at best and this unfortunately extends to pretty much whatever medium you choose.
When it comes to plane travel there are a number of domestic airlines to choose from, but Indonesia has one of the worst aviation safety records in the world and most carriers are banned from flying to the EU. Planes crash or have technical issues with alarming regularity here but the national carrier Garuda (which is no longer banned in the EU) is widely considered to be the safest choice.
Another popular way to travel between the islands in Indonesia is to take a boat but this is not much better than flying and ferries also sink regularly and regulations such as life jackets and other safety equipment are poor.
Bus transportation is popular amongst locals as it is one of the cheapest ways of getting around and the bus network in Indonesia is extensive although it can be confusing to navigate.
In tourist areas such as Bali hiring a motorbike is common and can be done illegally without a license although this means that you will probably not be covered by your insurance if you have an accident. You will also be committing a crime which could have serious consequences if you crash or hit someone.
Motorbike accidents among foreigners are frequent and often fatal, involving a combination of no helmet and large quantities of alcohol. Unless you have experience driving a motorbike then this is best avoided and if you plan to be a passenger then always wear a helmet.