Get Your Shots
The U.S. Centers for Disease Control (CDC) recommends getting a battery of vaccinations or boosters for travel to Indonesia, including Bali. The basics include the MMR (measles/mumps/rubella), DPT (diphtheria/pertussis/tetanus), and polio virus boosters. They also recommend shots for both hepatitis A and B, which is a good idea because these diseases are easy to catch. Also, since outdoor adventure usually means spending time in rural areas, shots for typhoid fever and rabies are a good idea. The risk of getting infected with either in Bali are quite low, but as long as you are getting shots anyway, it is a good idea to get these, especially the rabies shot. While Japanese encephalitis shots are also recommended by the CDC, the risk of catching this virus is very low, so much so that your health insurance might not even cover the shot.
The backcountry areas of Bali are marginally malarial, and urban areas are not malarial at all. Since the risk is very low, and given the substantial side-effects (reduced resistance to sunburn and/or strong nightmares) that sometimes result from anti-malarial medication, you should consider an anti-malarial prescription optional. If you do get such a prescription, check it to make sure your doctor did not mistakenly give you chloroquine, which is useless against the regional malaria strain.
But you should absolutely take strong precautions against mosquito and other insect bites. A good idea is to go to the camping store and get a bottle of deep woods repellent. American-made bug sprays of this kind strong concentrations of DEET, up to 98 percent in some cases. That is as much as three times stronger as what you are likely to find in Bali. It might irritate your skin after a few days, but it will definitely keep the mosquitoes away. It will also protect you against other insect-bite diseases like dengue fever.
Bali sits roughly 8 degrees south of the equator, making the sunlight there very strong even by tropical standards. Take the risk of sunburn very seriously while there, and be liberal about measures to protect your skin. Bring along a bottle of at least SPF 30 sunblock, as well as a good sun hat and the kind of light clothing that covers a lot of skin. Your attitude should be that if you aren't actively trying to get a tan, most of your skin should be out of the sun. You should also regard your sunblock as being somewhat less effective than advertised--those SPF ratings are determined using temperate climates as a basis, and the sun is weaker in Europe or North America than it is in Bali.
A popular backcountry activity on Bali is to hike up one or both of its two volcanoes, Gunung (Mount) Batur and Gunung Agung. There are guided tours available in virtually every tourist agency in Bali for these mountains, but a serious hiker will find the pace set by semi-fit tourists to be a big drawback and will likely want to go up independently. Unfortunately, the trails on these mountains are either poorly marked or unmarked, so hiking the mountains should be considered an exercise in orienteering. If you know you will be making a stab at either mountain, try to get your maps before you leave for Bali, and bring along either a compass or a GPS receiver.
Unless you are staying at a five-star resort that specifically advertises that its tap water is purified on-site, treat all the tap water as suspect. It doesn't need filtration, but it does need to be disinfected. You can either stick to bottled water, or you can boil the tap water or treat it with chlorine or iodine. Filtration and disinfection of local water sources will be necessary for backcountry camping, just as it would be anywhere else in the world.