It would be great if the app would remember that time it received an estimated arrival time and correct for the difference in time. Currently if the network is slow it displays an old estimated arrival time for sometimes a very long time, which can make one late fir the bus.
Alternately if the display was converted to an estimated arrival time via addition, and then the displayed value would not become increasingly incorrect as time passes.
The null check on selectedStopId should probably be followed by assignment to a local final int which is then referenced in the doInBackground callback.
It may not be appropriate to show a toast if the fragment is not attached to activity, anyway, though, so a simple null check on the return value of getActivity() would probably be best.