I just got back to NY from Bali . The first time i went to Bali was Sep 2001 , I am from NYC . I also was in Bali during 2nd bombing there, in Kuta sq and Jimbaran. Indonesia is a 3 rd world country , so one must always be aware ,mainly because of roads , fire exits , food etc.....
The people of Bali are awesome and friendly , in tourist areas sometimes a bit too much .. transport , massage etc.. ... To feel safer I guess you could avoid the big clubs ,and bars . Most places have 'security' , though it is far from perfect .

the people will never make you feel uncomfortable. The Balinese themselves are dependant on tourism, and are very aware of being a possible target ,with its many western tourists. All the previous acts were done by outsiders.

To feel extra safe i guess i would avoid main Kuta area , where the crowds are , and enjoy Ubud , or other quieter beach areas . I am going back , i would tell friends to go back too.