Seek to infer "correct" route from sequence of stops
To be clear, this is not an optimization problem; I do not seed to find the "best" route.


Actually this is an optimization problem!  Just instead of optimizing for shortest length or fastest time, you're optimizing for highest likelihood:


  What I seek to do is to infer what is most likely the intended route
   [...]


Now you just have to figure out your model for likelihood.

For example, say that the bus drives$$
\left[\mathrm{A}\right]{\rightarrow}\left[\mathrm{B}\right]{\rightarrow}\left[\mathrm{C}\right]
$$half the time, then$$
\left[\mathrm{A}\right]{\rightarrow}\left[\mathrm{C}\right]{\rightarrow}\left[\mathrm{B}\right]
$$the other half of the time.  But, it tends to do the first route on odd-numbered days, unless it's raining.  Except, the driver "Bob" reverses this pattern, whereas "Suzzy" always does the first one and "Atomic Robot #7" always does the second one.  What do you infer from that?

Math has no opinion on this topic.  For example, if you choose to believe that whatever "Bob" does is always correct, even if every other driver disagrees with him, that's your belief; math doesn't object.

So, what you need to do is construct a model for assessing how likely you believe a particular solution is given a set of data, then optimize for likelihood given the data.