Do the /user/bob style, as there's a very good reason why you should not use /bob.
Yes certainly with routing configurations you could allow this, so that /images/foo.jpg works and gives you the image "foo.jpg" in the image directory, but then /images would get you the user named images. That would basically be really confusing from the technical design perspective.
I know this isn't going to happen often, but in general it's just bad path design to have a scheme that you know can fail in some cases.
If you don't like the unfriendly naming of /user, try something else like /home or anything else you can think of that might be a bit less utilitarian.