Bacterial blooms and cycling generally occur at the same time but are not actually linked together. Bacterial blooms are the explosion of a free floating bacteria/protist. Nitrifying bacteria are sessile most of the time (attached to surfaces) and do not cause cloudy water. These explosions of bacteria are common in new tanks as the organisms colonize the tank. The OP has not started off a new "cycle". In a planted tank it is very common to have 0 nitrogen detected as plants can use ammonia, nitrite, and nitrate all directly.
There is an imbalance of nutrients in your tank at the moment. Do several large water changes (50% a day for 3-4 days) to remove most of the free floating bacteria/protist. Then begin with your fertilizer regimen. You may need to increase your dosage if your nitrate levels are that low. For a planted tank you need to attempt to keep your nitrates at 10-20ppm in order for you plants to grow well.