Assuming you have a cost attribute named "Minutes". Create a turn feature class with a field named "Wait_Minutes" and set a field evaluator for the "Minutes" attribute referencing the "Wait_Minutes" field. Then create a turn feature from bus line 1 to bus line 2 at the bus stop and set the "Wait_Minutes" value to be 10. Rebuild your network.
In that way, when the route requires traveling from bus line 1 to bus line 2, it goes through the turn and incurs and additional 10 minutes of travel time.
If all transitions are always 10 minutes, you can simplify it by using a constant evaluator of "10" instead of requiring a field and using a field evaluator...
matt