  We study epicyclic oscillatory motion along circular geodesics of the
Simpson--Visser meta-geometry describing in a unique way regular black-bounce
black holes and reflection-symmetric wormholes by using a length parameter $l$.
We give the frequencies of the orbital and epicyclic motion in a Keplerian disc
with inner edge at the innermost circular geodesic located above the black hole
outer horizon or on the our side of the wormhole. We use these frequencies in
the epicyclic resonance version of the so-called geodesic models of
high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars
and around supermassive black holes in active galactic nuclei to test the
ability of this meta-geometry to improve the fitting of HF QPOs observational
data from the surrounding of supermassive black holes. We demonstrate that this
is really possible for wormholes with sufficiently high length parameter $l$.
