There are several different species of bacteria that are involved in the nitrogen cycle. The anaerobic species are usually the slowest to colonize.
If referring to denitrifying bacteria, will case study the effectiveness of a bio pellet reactor. If properly sized, powered and filled these take about 30-45 days to fully colonize with bacteria added daily during that timeframe.
I would not rely on internal rock bacteria as your primary no3 removal. Other organisms(corals, algae etc) are more efficient at this. Depending on types of corals stocked this time frame for n2 production as primary no3 removal is probably 3-5 years less if have macro algae and certain soft corals.