The bronx is not a terribly dangerous place anymore, But still it's not a good place to be.
New York City is a massive place and a single borough such as the Bronx can be split into numerous different neighborhoods, some dangerous, some not.
If you want to stay safe while visiting Bronx, just follow common sense and here a couple big points I'd like to make
Try not to walk everywhere. If you go to the Bronx and start walking around that's taking a much bigger risk than getting cabs to your different destinations or renting a car for a few days.
Do not walk anywhere after dark. In a place like the Bronx you are probably safe walking around in the daytime, but walking around in the dark is definitely a bad idea.
If people are looking at you a lot, leave. It would definitely not be the first time a white guy got shot for no apparent reason
Be aware of gang violence in general. It was a very common occurrence for some random guy or women or sometimes even kids getting shot for wearing the wrong color shirt down the wrong street.
Again New York and the Bronx are not that bad like they used to be, but the bronx is still a dangerous place with more than it's fair share of gangs crime and danger.