In the default React Native app scaffolding you have to edit
AppDelegate.m to change where it loads the code if you want to test on your device. I use the following snippet to detect if it's being compiled for Debug or Production and for the Simulator or a device. For Production it uses a copy of the code included in the bundle, for Debug on the simualtor it loads from a server on localhost and for Debug on a device it loads from a server on a given IP address.
NOTE: You need to edit YOUR-IP-HERE and change it to the IP to load the code from when in Debug mode on a device. You could use a service like ngrok to make this work from anywhere.