The meaning of "observe" in "observe the bus stops"

Solution 1:

Meaning 2 in the Wiktionary entry for observe is the one you want:

(transitive) To follow or obey the custom, practice, or rules (especially of a religion).

The first example is:

Please observe all posted speed limits.

Here, the meaning is that the buses will stop at the bus stops on the diversion route.

This seems to be transport-operator jargon, and not something one would expect in spoken English, or in a well-written newspaper article. It's an example of the kind of "up-writing" we see when the author feels they need a more formal register, and believes this should be effectuated through illucidity. ;-)