Bernal Heights is considered far safer than the Mission to the north or the Hunter's Point area to the south (which together are considered 2 of the most dangerous areas in the city). However, if you look at actual crime reports--although there has not been a single murder in Bernal this year there have been over 500 assaults.
Put simply: you are still in the City and should behave accordingly--use common sense, don't go out alone for late night walks, stay alert when you are out and about, think about get a place with a garage so you don't have to worry about your car, etc.