Handle bus/train routes going off-map

I don't know yet how to model buses and map boundaries more reasonably. Right now, buses insist on making loops around the stops that're inside the map bounds. If the bounds cut off part of a route, then the bus does really strange things to glue together the two directions of the route. This is one of the main reasons why light rail in Seattle is hard; there's no way to turn around using the separate tracks except near the start/end of the entire route.

The more realistic thing is probably to have buses disappear/reappear at appropriate border intersections. But then some modelling questions:

1) How long should the bus spend off-map?
2) If someone is riding to a destination off-map, do we just measure the trip time to leave the map?
3) If someone boards near the end of the route and needs to ride off-map, then reappear and alight at one of the first stops in the other direction, how should that work?