A woman can become niddah from uterine bleeding even if it is not menstrual, so that factor does not affect this case.
However, mikveh use for conversion can take place while a woman is spotting. Her spotting should not preclude her immersion.
If she is bleeding heavily, and there are sanitary concerns, then arrangements can be made for the water to be changed after her immersion. If the bleeding is so heavy that she would be embarrassed, then common sense should be used in scheduling the immersion for a time when the bleeding is lighter.