How do I efficiently grow bioluminescent algae?
I have no experience with that particular species but dinoflagellates are often slow growing, very tricky to get to high densities and hard to maintain for a long time without proper experience and lab conditions. 

If you still want to have a go I would recommend the following. Growth conditions are rather similar for most dinoflagellates: use a rotary shaker (gentle rotation) in a 12:12 day night regime, don't dilute to hard when subculturing and use standard F2 medium (see link for recipe). If you cannot get hold of seawater you can use saltwater aquarium salts such as Instant Ocean. 

Most hate temperature changes so best to keep them at 18-21C