Some questions about Android and Google Directions Service:
Is there a native way on Android to use the Directions Service from Google or are there any nice
I don't know exactly if this is what you want, but you could fire up an intent like this:
String url = "http://maps.google.com/maps?saddr=some+address&daddr=another+Address"
Intent intent = new Intent(android.content.Intent.ACTION_VIEW, Uri.parse(url));
To get biking directions add "&dirflg=b" to the url. For public transport add "dirflg=r".
This will display the route in the google Maps app. If you want to get this in your app inside a mapview, please see this code at github. You could hack into the code to add biking and public transport functionality.
Hope this helps somehow.