Modes of transport in Bali:
Walking is best when you get to an area you want to check out, rather than getting to that location. I would add though, that the idea of taking a month and walking through some of the mountainous areas would be fun.
Pros of this are that it is free, you have maximum time to appreciate your surroundings and interact with locals. Cons are that you can’t travel far in a short time and it can be exhausting.

Bicycle - Riding:
Bicycle - Riding a bicyle is non-polluting as far as air and noise and makes to totally accessible to interactions with locals.
Pros of riding a bicycle are rather like walking, except you can cover more ground. One of the nicest bike trips you can make is to start from a mountainous location, taking only quiet roads back to Ubud, or a place at a lower elevation. This would allow you to cruise through villages and save your energy.
Cons of riding a bicycle are traffic, climate, terrain and sun. Bali has an ever increasing army of motorbikes, which together with cars, buses and trucks cram streets and pump out a lot of pollution. Riding in this environment is not pleasant. In Bali you will sweat just drinking a cup of coffee. Riding a bicycle miles up hill, you will be soaked and exhausted, not to mention cooked by the searing sunlight

Motorbike / scooter:
Motorbike / scooter - Now we’re talking! This is the most popular means of transportation for people in Bali, both local and foreigner. Motorbike rental can be as cheap as 400,000rp per month, which is what I pay, for a Honda Supra scooter. You might pay 40,000rp per day. There are various scooters available, from the 100cc Honda Supra Fit to the 125cc Honda Karisma. Each can carry 2 people and are adequate for exploring lowland areas. I have ridden all over Bali for th past 3 years on one of these scooters. For larger people, or people who plan on riding to the mountains, 2 on 1 bike, you might want to rent a Honda Tiger. This 200 cc motorbike actually looks like a proper bike and has adequate power. You might rent one of these for 75,000rp a day. Surfers can inquire at rental places about getting a surf rack fitted, to accommodate the surfboards. This should not cost extra and if the fittings are in place they can add the rack in 10 minutes. Pros for using a scooter / motorbike are ease of movement over a car, due to the manoueverability of the motorbike. Ease of parking, affordability, great mileage, ability to reach all of the island in one day and ability to have a more personal contact with your surrounding than sitting inside an SUV.
Cons are risk of accident, more expensive than walking, you add to the pollution of the air, not as organic as walking, not as comfortable as riding in a car, exposure to sun / weather.

Car:
Car - There are a selection of vehicles that are available for rent. These range from the small Suzuki Katana or 65,000rp per day to the new Teruna which might go for 350,000rp per day. The larger the load and larger the passengers, the bigger the vehicle should be. Believe me, its worth spending more to be comfortable, although I can be comfortable in a Katana, with just 1 other person.
Pros - You can haul a group of people and their gear anywhere in Bali. You have protection from the elements and other vehicles.
Cons - Higher cost than renting a motorbike, harder to get through traffic, harder to park, not as ‘organic’ as riding a bicycle and less personal than a motorbike.

Taxi - Taxis are widely available in all city areas. While okay for short trips, they can be relatively expensive when you start adding up the miles.
Pros - Someone else does the driving, super easy to find, no parking or traffic stress.
Cons - Relatively expensive. Leaves you without transport when you get dropped off.

Car with driver - Very easy to arrange in Bali. Most car rental places have friends who are willing to drop everything and be a driver or a day or 2. Hiring a driver will mean adding on maybe an extra 50,000rp a day to your car rental. A day means 10 hours and the person will find their own accommodation. You should help them out with this if you are taking them on a multi-day trip, give a small amount extra for food and accommodation.
Pros - You have the freedom of your transport and don’t have to drive.
Cons - You have an extra person along on your trip.

Bemo A Public Vehicle:
Bemo - This is the X factor in Bali. I remember back in 1993 many backpackers used to take bemos, the small local buses that run set routes, but with no schedule.
Pros - You can get around Bali by a wacky route of villages, stopping to pick up locals along the way. You are packed in tightly with locals and get face to face interaction. No need to book, or plan in advance, just flag the bemo down and climb aboard.
Cons - You have to bargain every time to use a bemo, or get charged several time the correct fee. This can be maddening and exhausting. Bemo’s are not comfortable and in the past I have had a local woman plonked on my lap, as the bus gets filed up. There is no chance to stop for that picture postcard photo.

Perama bus. Perama operates minibuses to tourist destinations like Lovina, Ubud, Candi Dasa. They will drop you off for a set fee, at a set time. After that its up to you.
Pros - Set schedule and fees. Comfortable and reliable.
Cons - More expensive than renting a motorbike with no further transport when you reach your destination.

Day tours - Anyone staying in the main tourist areas will come across places offering day tours. Indeed in most cases hotels have a ‘tour desk’ arranging these.
Pros - You can get away from the tourist areas / your hotel, for a day and see a completely different part of Bali. It take very little mental energy to book / take a day tour.
Cons - You are getting sold a package. The people who are selling the package want a ‘cookie cutter’ way to make money. They will take you from one ‘attraction’ to the next, same as all the other tour companies. You could spend the majority of the time in the van getting to places, rather than exploring them.

Whatever form of transportation you choose, will have a massive impact on the type of experience you have in Bali. Some people choose not to have any transportation and just stay around their hotel. That dictates the kind of experience they will have.

As a closing though I’d say that you can make all of the options above work to a degree in certain situations. Your length of time and comfort level as far as exploring will be 2 big factors. Renting a car with driver, flicking through a guidebook and being a bit adventurous will pay dividends, for first time visitors to Bali.