You can still have 2 buses service a stand. Just assign one of them to a stand, and the other in a lot/depot near the stand’s assigned bus stop. The bus assigned to the stand will always take the arriving passengers, and the extra bus from the depot/lot should be dispatched if the other bus is still performing a task. If the first bus is free, however, that one will get the task of loading the departing passengers.
I know there had been issues in the past where if you have that kind of set up the bus for the departing passengers would arrive at the bus stop before the bus for the arriving passengers, but I believe the devs said they fixed in (not sure if it is fixed in just the experimental branch, or all branches).
Regardless, I have always experienced that if you have a 2:1 ratio of buses to stands, the second bus should kick in, when necessary. Just make sure you help it along with the best route possible (shortest routes, with least amount of turns).