2. a and b are usually interchangeable. Take is used more often in the imperative, I think. You tell someone "Take the bus" but you answer the question of how you got to work with either, "I take" or "I ride" the bus.
c. get in/on - means to actually climb aboard, and either works gramatically, but I think "on" is more common in speech. We do actualy get inside, but on suggests that we are there for the ride. I think of getting on the bus as if I am riding some continuous pathway, like a moving sidewalk; I am on the path, as I am on the bus.
d. Again, both are correct, but generally we don't use either in or on, with ride. That is implied. You simply "ride the bus to work." Even when the riding is more active, like riding a horse or a bike, we still simply ride it, we don't say we ride on it.
The "on" comes into play when the object or position is described in more detail. We "ride on the back of an elephant," for example; not, "ride the back of an elephant."