There is no need to bring down nitrite level. Quite the opposite, you need the nitrite to develop the bacteria species feeding on nitrite.
As you know, the whole nitrite cycle is: Ammonia --> Nitrite --> Nitrate
Nitrate is the end product of the cycle, not nitrite. If you remove nitrite, the cycle won't be completed.
You are doing it right so far (if you haven't done any water change to remove the nitrite) and making good progress as well.
The only time you need to do partial water change during a fishless cycling is to bring the PH up in case the PH crashes (sudden large drop) due to too much nitrate was produced. Too low PH can stall the cycle because the bacteria do not like acidic water.
If you have read our article on aquarium nitrogen cycle, you should know that you are at least into the second stage of fishless cycling. It is a good sign that you have nitrite. You should start to test for nitrate.
Once again, do not remove nitrite nor ammonia. They are "raw material" needed to complete the cycling process.
