Yes, AZ has a bonus point system.
Here is how it works:
First pass is the 20% pass were the applicants with the most Bonus points are issued tags up to 20% of the total tags for each unit. (NR only receive up to 10% of the total tags and that restriction is generally met for units considered to be trophy units during this phase of the draw process.)
In the second pass, the AZGFD generates a random number for every point you have plus an additional point for your application. (first year no points you get one number. Second year one point you get two numbers) Your lowest number is kept and all others are thrown out. The applicant low numbers are then sorted and the lowest numbers are compared against the 1st and 2nd choices on all applications. If tags are available for your 1st or 2nd choice when your number comes up, you get a tag. If not you are placed in the second draw pool.
The second Draw is handled just like the first with new numbers generated and all but your lowest thrown out. The low numbers for applicants in the second pool are sorted and if tags are available for your 3rd, 4th or 5th choices, you get a tag. If not, you are unsuccessful and given a point for the next years drawing.
As stated above, NR tags are limited to 10% of the total tags per unit, per hunt and the trophy area hunts such as units 12 and 13 for deer and units 9 and 10 for elk reach the NR limit during the 20% draw process. When you hear "Max Points" from NR's this is what they are talking about. Most of the elk units have quality elk so you should be able to draw a decent unit within a few years if you don't have to have a highly desired unit.
Everyone must purchase a general hunting license to apply for a big game tag and the NR license fee is $151.25. The applicaiton fee is $7.50 so if you apply for Elk, Antelope and Deer your total cost would be $173.75. If you are drawn your CC will be charged for the tag and current NR fees are Elk - $595, Antelope - $485 and Deer - $232.75.
Hope this helps
ELHTR