You give your patient as much O2 as THEY need, no more, no less. A patient hyperventilating from a panic attack doesn't supplemental O2, but you had better be sure of the cause, as a PE, MI, pulsed VTach, SVT, or an overdose might give you the same hyperventilating anxious look, but these patients may very well need a NRB mask or nasal cannula, in addition to other emergency treatment.
I think about it this way. When you approach a new patient, you start with a first impression. Are they in respiratory distress? If so, O2. If not, begin taking basic vitals which will hopefully include SPO2. These vitals may give you insight as to the patients emergent condition, they may not.
I like to come up with a goal for my patient's O2 saturation. An elderly COPDer is good anywhere over 90% with no respiratory distress, though I would like my young and healthy patients to sat over 95%. One hundred percent O2 saturation is not your goal.
And going with the other commenters, a BVM should be used with O2 if available, as you only only use them for patients in severe respiratory distress or failure, so no matter how much oxygen you put through their airway, there body is having a problem using it and we'd give them 110% if we could. That said, no overzealous bagging, that causes gastric distension and barotrauma, which are bad...mmmkay?