Basses don't normally use reentrant tunings, so I think we can ignore ukuleles and banjos and so forth. Of course, bass ukuleles do exist, but they're normally tuned the same as the bass guitar.
A bass's top string is the one highest in pitch, so the one closest to the floor in a normal playing position. I know some people call that the bottom string because they're talking about physical location not pitch, but those people are wrong.
A bass's strings are numbered from highest pitch to lowest starting at 1.
The top of the bass or guitar neck is the end that joins the body, i.e., where the highest pitched notes are found, and the bottom of the neck is the nut end. Obviously this is opposite to how a person or animal's neck would be described: deal with it.