With "come across" to speak of a chance encounter with another person, I believe we are dealing with nuance, a slight difference in meaning, or a more specific idea. This would not be the first thing to come to mind, and dictionaries probably don't account for it.
Generally, using "come across" to speak of people, usually implies, or means a much more unexpected, very chance, or much less likely encounter. So it is possible to use "come across" to speak of people, but this is a lot less frequent than "bump into" (or "run into"), which is the more usual expression for a chance or unexpected encounter with another person.
Also, in speaking of "coming across a person", we can imagine a crossroads or an intersection. What would be the chances of crossing an intersection and meeting someone you know or have not seen for a long time? The chances would be very small. So "come across" seems to imply two separate points coming together in one place, which seems to be rather unlikely but still possible. On the other hand, "bump into" gives us the idea of more open space, not limited to "across" or "a crossing point", thereby making it seem that such a meeting is not such a distant or a remote possibility.
In other words, it seems a lot less likely that two points, or two people, would come together exactly where two roads cross each other (come across). By contrast, "bump into" seems to tell us that the space is open (not limited to a point where two lines cross) and the possibility of a chance encounter with someone is somewhat less distant or less remote.
It's true that, more often, "come across" is used to speak of objects of any type and animals.
We should also remember that "come across" can also be used to speak of an impression someone leaves or how someone projects their personality in a given situation.