Yes, there is an airport in Bali, it was known by the name of Ngurah Rai International Airport

Below I am providing you details of this Airport to you:

Ngurah Rai International Airport also known as Denpasar International Airport, is the main airport in Bali, located 13 km south of Denpasar.

It is the 3rd busiest airport in Indonesia after Soekarno–Hatta International Airport and Juanda International Airport.

The airport has category IX and is capable of serving aircraft up to the size of Boeing 747-400

Other details of this Airport are:

Contact Details:
Ngurah Rai International Airport  
Jalan Raya Gusti Ngurah Rai,
Bali 80362, Indonesia
Phone: +62 361 9351011

Code: DPS

Elevation: 4 m

Airlines and destinations

Airlines Destinations
Air New Zealand Seasonal: Auckland
AirAsia Kuala Lumpur
Asiana Airlines Seoul–Incheon
Asia Atlantic Airlines Bangkok-Suvarnabhumi
Air Niugini Port Moresby
Air Timor Dili
Batik Air Balikpapan, Bandung, Jakarta-Halim Perdanakusuma, Jakarta-Soekarno-Hatta
Cathay Pacific Hong Kong
Cebu Pacific Manila
China Airlines Taipei–Taoyuan
Seasonal: Kaohsiung
China Eastern Airlines Shanghai–Pudong
Seasonal: Beijing–Capital
China Southern Airlines Guangzhou, Shenzhen
Citilink Bandung, Balikpapan, Jakarta-Halim Perdanakusuma, Jakarta–Soekarno–Hatta, Surabaya
Citilink Dili
Charter: Chongqing
Dragonair Hong Kong
Emirates Dubai-International
EVA Air Taipei–Taoyuan

Seasonal: Kaohsiung
Garuda Indonesia Bandung, Jakarta–Soekarno–Hatta, Jayapura, Kupang, Makassar, Manado, Mataram–Lombok, Medan, Palembang, Semarang, Surabaya, Timika, Yogyakarta
Garuda Indonesia Beijing–Capital, Dili, Guangzhou, Hong Kong, Melbourne, Osaka–Kansai, Perth, Seoul–Incheon, Shanghai–Pudong Singapore, Sydney, Tokyo–Narita
Garuda Indonesia Banyuwangi, Bima, Ende, Labuan Bajo–Komodo, Mataram–Lombok
Hong Kong Airlines Hong Kong
Hainan Airlines Beijing-Capital
Indonesia AirAsia Bandung, Jakarta–Soekarno–Hatta, Solo, Surabaya, Yogyakarta
Indonesia AirAsia Bangkok–Don Mueang, Darwin, Kota Kinabalu, Kuala Lumpur, Perth, Singapore
Indonesia AirAsia X Jakarta-Soekarno-Hatta
Indonesia AirAsia X Melbourne, Sydney
Jetstar Airways Adelaide, Brisbane, Cairns, Darwin, Melbourne, Perth, Singapore, Sydney, Townsville
Jetstar Asia Airways Singapore
Kal Star Aviation Ende, Kupang, Maumere, Pontianak, Surabaya
KLM Amsterdam, Singapore
Korean Air Seoul–Incheon
Lion Air Batam, Bandung, Jakarta–Soekarno–Hatta, Kupang, Mataram–Lombok, Makassar, Manado, Medan, Yogyakarta
Lion Air Charter: Chongqing, Hong Kong
Malaysia Airlines Kuala Lumpur
Malindo Air Kuala Lumpur
Nam Air Surabaya, Maumere
Orient Thai Airlines Charter: Phuket
Philippine Airlines Manila
Qantas Seasonal: Sydney
Qatar Airways Doha
Royal Brunei Airlines Bandar Seri Begawan
SilkAir Singapore
Singapore Airlines Singapore
Shanghai Airlines Shanghai–Pudong
Sriwijaya Air Jakarta-Soekarno-Hatta
Sriwijaya Air Dili
Thai AirAsia Bangkok–Don Mueang
Thai Airways Bangkok–Suvarnabhumi
Tigerair Singapore
Tigerair Australia Adelaide, Melbourne, Perth
TransNusa Air Services Bima, Ende, Kupang, Labuan Bajo–Komodo, Mataram–Lombok, Ruteng, Sumbawa Besar, Tambolaka
UTair Aviation Charter: Moscow-Vnukovo, Novosibirsk
Virgin Australia Adelaide , Brisbane, Melbourne, Perth , Port Hedland, Sydney
Wings Air Bima, Ende, Kupang, Labuan Bajo–Komodo, Malang, Mataram–Lombok, Maumere, Semarang, Surabaya, Tambolaka, Waingapu
XiamenAir Xiamen