The best app to find out when the next bus is coming is Citymapper. It handles tubes and trains too, but it’s with buses that you get information you don’t get at many stations.
It tells you how many minutes are left until the next bus comes, even if the station you’re at does not have a display. You can setup your favourite journeys too, such as to and from work, so that you can easily check out times before you even set off for the bus stop.
Citymapper also has a journey planner function, which is very useful if you’re not familiar with the local bus routes. Citymapper is completely free to download and use.