When do neutrophils enter the blood from the red bone marrow in response to leukocytosis-inducing factors?

The right answer is during leukocytosis.

Leukocytosis is an increase in white blood cells including polynuclear cells (neutrophils, eosinophils, and basophils), monocytes and lymphocytes. This increase is due to physiological factor (sport, stress, pregnancy ...) or pathological (inflammation, infection, leukemia ...) that is called leukocytosis-inducing factors.