You do need to include $PATH in each of those lines in your .bash_profile otherwise you'll lose the default paths (including /bin, which is where bash is installed by default on OS X).
As this stands, without $PATH on the second line of your .bash_profile, you're completely overwriting your previous path with "/usr/local/bin:subli". Then the third line adds "$HOME/.rbenv/bin" in addition to that, but you're still going to be missing things like /bin, /usr/bin, etc.
I would go ahead and make sure that you are including $PATH in all three of those lines so that you add to, rather than replace, your existing path.