Slash chords which use a note that is a part of the main chord as the bass note are called inversions. Common open slash chords are:

A/E:  002220
C/E:  032010 or XX2010
C/G:  332010
D/A:  X00232
D/E:  0X0232
D/F#: 200232
E/G#: 4XX454 - weak
F/C:  X33211
F/G:  XXX011 or 120011 if you are elastic enough
G/B:  X20003

5-string pattern for third in bass:

Find the bass note (third), bar two frets lower, play X20003 (where 0 is your finger) or X2000X. For a funky (but incorrect) sound, play X20000 which is strictly G6/B (or transposition thereof).