Citymapper et al are excellent. The big issue I find is that half the time TFL seems to completely ignore its own bus schedule (at least in my area). You rush for a bus and it leaves 2mins before schedule (and the next one also turns up early). I would rather longer waits and better predictability.
In my previous town I had a bus so unreliable I'd rather walk 20 minutes in the sub zero temperatures - was supposed to run every ten minutes, but in reality there was no bus for an hour and then 5 in quick succession.