Ostensibly is the adverb that belongs with ostensible. If something is ostensibly true, that is the story people tell, but you are being invited not to swallow it whole. “She was ostensibly working late” means that is what was said; the speaker thinks something else was going on. “The club is ostensibly open to everyone” means that is the official line; in real life it may not work that way. The word does not mean “obviously” or “clearly” — though actually, learners often hear the os- and think it is a posh way to say “plainly”. It is closer to the opposite: so they say. Same formal tone as ostensible. You will hear it from news readers, teachers, and people telling a story with a raised eyebrow, not from small children. The matching adverb for showing off is ostentatiously, not this word.