The question is not so much about the usage of "whom", I think, but rather, the use of "to".
The verb 'offer' can have two objects ; You would offer / him / the ride. If this sentence is changed into a question, it will be like this ; Whom would you offer the ride? In this context I can't understand why Preposition 'to' should be added into this question... - tasmantiger comment above.
Indeed, in your sentence "To whom would you offer the ride?", the verb "offer" takes two objects: "whom" and "ride". The point is that one (the ride) is a direct object, while the other (whom) is an indirect object.
We can see this more clearly if the sentence is written (more simply?) with the indirect object after the verb:
You would offer the ride to whom?
Now we can see that "to" serves to identify "whom" as the indirect object. The "ride" is offered directly and has no need of a preposition. So, if we move "whom" back to the front of the sentence, it either takes its "to" with it, to show it's an indirect object...
To whom would you offer the ride?
... or (and to be more relaxed about the structure - thanks, keshlam) you can leave the "to" at the end:
Whom would you offer the ride to?
For more information, see here: Write.com - direct and indirect objects.