Whilst it is possible to legally marry in Bali, it is a complicated process that does come with many restrictions. Its common practise for couples having Destination Weddings in Bali to take care of the ‘paperwork’ in their home country.
Quoting a Government website, “persons of any nationality may marry in Indonesia provided they both hold the same religion recognised by the Indonesian Government (Islam, Hinduism, Buddhism or Christian) and their celebrant or officiant must be a Minister of Religion, officer of the Civil Registry Office (Kantor Catatan Sipil) or the Office of Religious Affairs (Kantor Urusan Agama).”
Religion:
It is possible to get married in Bali legally, but you both have to be Islamic, Buddhist, Hindu, or Christian, and have a ceremony according to that faith.
Same Sex Marriage:
It is currently not possible for same sex couples to legally marry in Bali.
Celebrants:
If you choose to make it legally offical in Bali, you will requite the presence of a Indonesian citizen, meaning most likely not your local ex-pat choice. The Balinese culture and people are beautiful and there are many local choices for officiants should that be the path you wish to choose.