Need mapquest-type app, bus schedules

Bus info for Zurich is at www.zvv.ch and for Bern at www.bernmobil.ch.

While someone else probably has a favorite app to recommend to you, I'll suggest the old-fashioned methods, which Switzerland is particularly good about. The Tourist Information Office in each town should have a wealth of handouts for you, and paper city maps will be available there and in hotels. Maps at bus stops and directional signs on popular street corners should be common. Where you might use an app or even a paper map more is when staying in suburbs or venturing further from the main tourist path.

I've used Google Maps and the Apple Maps on my iPhone in France, Germany Italy, Spain and Portugal with great success. Never considered finding another app. I'm confident they'll both work well in Switzerland.

I recommend http://timetable.search.ch/
It will do from and to any address in Switzerland.
The Swiss railways site: www.sbb.ch will also accept addresses as well as railway stations.
Both will show you walking route to nearest public transport, then public transport from there.

Yeah the Swiss Rail site/app does it all. Train/Bus/boat/cable car schedules, including walking directions.
You don't even need to know the address, you simply type in the name of the hotel or any other landmark or attraction.