Ok so this has not been an easy thing to translate however hopefully my friends and I have done it. I am regularly asked about gluten free suggestions for eating in Bali, I have compiled a few ideas however I am sure there are so many options available for you. I think you will be pleasantly surprised how many places now have GF on the menu or if you discuss with the chef and the staff they can make some adjustments or perhaps even bring you out a special menu at some places. One tip is also to ask the chef to swap soy ( kechap aisin / manis ) soy sauce for fish sauce, and stick to fruit, veggies, etc and you should be fairly safe.

Here is a translation which you can copy/print out and take with you which may also assist.

English – I have been diagnosed with a medical Coeliac disease and I must eat a strict gluten free diet. I can not eat food that contains wheat, rye, barley or oats, such as pasta, couscous, breadcrumbs, batter, bread, pastry, cakes, biscuits or noodles unless they are specifically made using gluten free flours, please check the ingredients for processed meats, soups, sauces, gravies, dressings and custards. I can eat a variety of foods including unprocessed meat, fish, fruit, vegetables, dairy products, rice, corn (maize), polenta, lentils, soy and potato. If you have any questions when preparing my meal please ask me. Thank you.

Indonesian – Saya telah didiagnosa medis sebagai pengidap penyakit Coeliac dan harus makan makanan yan seratus persen bebas gluten. 
Saya tidak bisa makan makanan yang mengandung gandum, gandum hitam ( rye), jelai ( barley) dan haver (oats) septerti pasta, ( spaghetti dsbnya) couscous, remahan roti, adonan tepung, roti, kue kering (pastry) kue, biskuit, mie terkecuali, terbuat dari tepung khusus yang bebas gluten. Harap periksa bahan- bahan dalam daging olahan , sop, sause, kuah, minyak salad dan via ( custart).
Saya Boleh makan berbagai jenis makanan termasuk daging yang tidah di olah, ikan, telur, buah – buahan, sayur- sayuran, produk yan mengandung susu, nasi , jagung, polenta lentil kedelai dan kentang. tidah di olah. 
Jika ada pertanyaan saat menyiapka makana saya harap tanya saya terlebih dahul. Terima Kasih.

So here are a few restaurants and cafes which seem to be fairly up with this:

Canggu ~

Oka’s Bakery

Canggu Deli
Bungalow Living in Jl Berawa
Betelnut Café Canggu
Bali Buda in Ubud, Kerobokan and the Bukit

Seminyak ~

The Deck at the Semara Resort & Spa Seminyak
Petitenget on Jl Petitenget, Seminyak
The Living Room on Jl. Petitenget 2000, Kerobokan
Cocoon Beach Club in Seminyak
Ku De Ta in Seminyak
Sarong (has its own GF menu ) Jl. Petitenget No. 19X, Kerobokan Bali
Wild Orchid at the Anantara Resort Seminyak
La Lucciola onJl. Kayu Aya, Seminyak
The Bali Bakery in the Seminyak Square
The Bali Deli on Jl. Kunti 117 X Seminyak
Biku on Jl Petitenget
The Earth Café on Jl Oberoi
Zula in Seminyak
Mamasan on 

Jl. Raya Kerobokan No. 135
Br. Taman
Blue Karma Resort in Seminyak
Taco Beach Grill on 

Jl. Kunti 6, Seminyak.

Sanur ~
Dusk Blue Café  on Jl. Duyung 3 Sanur
Manik Organik in Sanur

Kuta ~

Poppies Restaurant Kuta
Dijon in Kuta – Poleng Mall – Blok A1-2, Jl270186

Ubud ~

Café Wayan Jl Monkey Forest Ubud
Plantation Restaurant at the Alila Resort Ubud
Indus Restaurant on Jl Raya, Sanggingan, Ubud
Como Shamabala on Jl Raya Sanggingan, Banjar Lungsiakan, Kedewatan
Alchemy in Ubud.
Down to Earth Market and Restaurant in Ubud
Alila Ubud
Kue inJl Raya Ubud

Candidasa ~

Alila Manggis Candidasa