The Island of Bali is an ideal destination for introvert travelers for some reasons:
The first is the smiles, friendliness, and the hospitality of local Balinese people as the hosts. In general, the people are warm and open; some of them have lots of stories and are happy to share it with you when you are polite and respectful.
Second is its culture and atmosphere. The ceremonies, the way of life and pearls of wisdom are eye-opening when we can do the first thing above. I, personally, feel being reminded about the invisible relationship between human-nature-God when I see a small temple or canangsari, even in the most modern establishments.
The third is the varieties of places to visit and things to do. Most likely, Kuta, Legian, and Seminyak are not on your top list, but Bali has Ubud, Bedugul, Kintamani which offer something more acceptable for introverts. In addition, the accommodations, for example, offer an abundance of choices to suit your preference, as well as the destinations.
As a good beginning, this list of 5 places for introverts cost you almost nothing but your curiosity to follow the road (well, some places cost you a small amount of parking fee and entrance ticket).
Or, you might tempt to taste delicious and affordable seafood lunch and experience a laid-back day at Lebih Beach Bali.