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Any future employer must prove you can do a job no local is available for in order to get a work permit.
That will cost them US$1,200 per year plus the immigration stuff (not too much), and they'll expect to pay an expat salary, that commonly being 5 to 10 times that of a local.
That limits you to top hotels/restaurants if you can find one willing to hire foreigners.

Assuming you have skills unavailable from an Indonesian, try the big hotels.

Hi Andy,

Try the big hotel chains such as Marriott Group which are huge as they keep buying other hotel chains and the Accor Group. There are definitely western chefs in some hotels and restaurants, and probably some western chefs who either own or part own businesses in Bali. But as the above poster mentions, many of these jobs are being filled by local Indonesians which overseas experience in the hotel chains.

If you want to succeed in Asia then as already suggested the big chains are the ones to go with but it might be useful to also contact these chains around Asia and build up a reputation so that you are in demand and then it would be easier to work here. Bali is full of hotels, chefs, and those trying to be chef in those hotels. You have to stand out from the crowd and have something that will make the hotel need your services. It a tough one really.

You could also try to apply for jobs in Indonesia as well so that again your skills will be more relevant and head to Bali, again in time.

What has already been mentioned is accurate as it pertains to Bali. 

Aside from executive chef positions in tier 5 star resorts on Bali such as the Four Seasons, the various Aman Resorts, etc., there is very little opportunity for employment here in Bali as a chef for the simple reason that there are a number of schools teaching the culinary arts here on Bali, and there are a large number of very qualified Balinese chefs available for employment.  Even non Balinese Indonesians find the competition for chef jobs to be competitive. 

Most foreign chefs you run into on Bali are in partnership business arrangements with Indonesian owned restaurants or other than 5 star resorts.

Thanks for the feedback.
Much appreciated

Andy