Our long-term photometric monitoring of southern nova-like cataclysmic variables with the 1.3-m SMARTS telescope found BB Doradus fading from V \sim 14.3 towards a deep low state at V \sim 19.3 in April 2008 . Here we present time-resolved optical spectroscopy of BB Dor in this faint state in 2009 . The optical spectrum in quiescence is a composite of a hot white dwarf with T _ { \mathrm { eff } } = 30000 \pm 5000 K and a M3–4 secondary star with narrow emission lines ( mainly of the Balmer series and He i ) superposed . We associate these narrow profiles with an origin on the donor star . Analysis of the radial velocity curve of the { \mathrm { H } \alpha } emission from the donor star allowed the measurement of an orbital period of 0.154095 \pm 0.000003 d ( 3.69828 \pm 0.00007 h ) , different from all previous estimates . We detected episodic accretion events which veiled the spectra of both stars and radically changed the line profiles within a timescale of tens of minutes . This shows that accretion is not completely quenched in the low state . During these accretion episodes the line wings are stronger and their radial velocity curve is delayed by \sim 0.2 cycle , similar to that observed in SW Sex and AM Her stars in the high state , with respect to the motion of the white dwarf . Two scenarios are proposed to explain the extra emission : impact of the material on the outer edge of a cold , remnant accretion disc , or the combined action of a moderately magnetic white dwarf ( B _ { 1 } \lesssim 5 MG ) and the magnetic activity of the donor star .