How can I make my shell prompt show the working directory relative to an arbitrary directory?

Suppose I do a lot of work under the directory /home/user/documents/foo, so the Bash shell prompt could appear as follows:

user@hostname: ~/documents/foo/bar/baz $

My terminal is quite narrow, and the ~/documents/foo is not a helpful use of space, since I already know I am there. I would therefore like my shell prompt to show the working directory *relative to* /home/user/documents/foo:

user@hostname: bar/baz $

The prompt is defined by the PS1 environment variable, and I can find ways of editing this to include the path relative to my user's home directory, or to include only the basename, but I can't seem to get a path relative to a different directory.