In the French language, when I meet someone, I decide whether I am going to use the polite form or familiar form. I usually stick to one. I don't go switching back and forth between them.
In Japanese, people often switch back and forth all the time. This is very tough to learn, but there is no logical way to really learn it other than just to get a lot of experience with the language. It's not just a simple matter of polite or familiar forms. I would say that each way of using polite or informal speech has it's own feeling of a level of politeness or familiarity, and what is used may depend on the feeling that the speaker had at the time.
If you want to be strictly polite, always use "desu" and "masu". As with most languages, the risk you take is to come off as too stiff and alienate people with whom you could have been more familiar. It's when you have human relationships that fit into a certain gray area between formal and familiar where you see the most mixing of different levels of politeness/familiarity. Examples are the employee who is quite friendly with the boss and the sushi chef who is friendly with the customer.
"Masu" for some reason is more stiff and formal sounding than "desu". I use "desu" (usually softened with a "ne") with people who I just met who are around my age, but never "masu". I only use "masu" when speaking to staff of a store or people older than me whom I don't know.
"Karadesu" sounds very stiff and formal for some reason. "Desukara" doesn't sound any more stiff than using "desu" in general.
These omissions are not to introduce vagueness. I do think that the way Japanese is generally used is slightly more vague than how English is usually used, but don't listen to a lot of the beginners who harp on about Japanese being too vague because they actually just don't understand it.
Also, in the specific example of "じゃあ、早稲田まで," I don't know why, and maybe someone else can explain it, but adding "desu" would sound weird there.
When you said "I feel that this sentence is in plain form as the subordinate feels superior to the driver due to a perceived difference in social status," I think you're overthinking that.
As I imagine you have read, leaving out the masu and desu and using the familiar forms of verbs is, well, the familiar way. Do this with your friends. On occasion there are friends who use "desu" with me, but usually not. You might see two Japanese friends using "desu" together almost all the time. I don't pretend to understand it. I've never seen two friends using "masu" together.