I checked with my wife and the Bonus WAS a monthly cash payout to folks and depending on when you became eligible the amount varied (I think) or else the eligibility age was increased for a while then terminated.  At any rate, the program was supposed to sunset and the number of eligibles was diminshing fast.  The whole thing was ended a couple years ago by the current governor.  Some sort of needs based assistance with perscriptions was eventually provided as a small consolation.
There was also a primary residence tax forgiveness program during the peak of oil wealth.  At one time I think the state reimbursed the cities for lost revenue but eventually dumped it on the municipalities. I think some have retained the benefit while others haven't.  
So far all who can show they have lived in Alaska for a specified time period can qualify for the annual  permanent fund dividend. The dividend has recently ranged from about $900 to nearly $2,000 per person - here is a link for more accurate information.   
http://www.pfd.state.ak.us/But before you rush to AK for the big bucks remember  here in the bush, I pay $3.49 / gal for gas,  about $2.60 for heating oil (and I use a lot), milk is $6.49 a gallon and rents run $ 950 to over $1,300 /month for modest apartments and houses.  Now its quite a bit cheaper in Anchorage but most other places living and travel expenses are substantial.
HTH