Per the Suggestion spell, on a successful save the target "is unaffected and thinks you were talking to them normally, not casting a spell on them." Only on a critical success does the target know you tried to control it.
So what about bystanders? Suggestion has somatic and verbal components, but are they obvious to bystanders as a spell being cast (in which case a success by the target resists the compulsion but not an implied "you don't realize I'm casting a spell on you" effect) or are bystanders unaware that a spell was cast unless they see the effects on the target? The former would eliminate the usefulness of the Conceal Spell feat, but only in this very particular case, so I'm not sure which way to go on this.