  We present a detailed photometric study of the bright cataclysmic variable BG
Tri using ground-based observations mainly from Rozhen Observatory, ASAS-SN,
TESS, and WASP sky surveys. We report the discovery of a negative superhump
with P$_{-sh}$ = 0.1515(2) days and a co-existing superorbital variation with
P=3.94(53) days in data from 2019 and 2020. A positive superhump with P$_{+sh}$
= 0.1727(14) days is also discovered in data from 2006. The obtained negative
superhump deficit $\varepsilon_{-}$=0.044(1) and the positive superhump excess
$\varepsilon_+$=0.090(9) give us an independent photometric evaluation of the
mass ratio (q) of the system, which we find to be q$_-$ = 0.37(2) and q$_+$ =
0.40(5) respectively. We also present a study of the quasi-periodic
oscillations (QPOs) and stochastic variability (flickering) in BG Tri. The
light curves show a rich mixture of simultaneously overlapping quasi-periods
ranging from 5 to 25 minutes. The multi-color (UBVRI) photometric observations
from Rozhen Observatory reveal the typical increase of the flickering
amplitudes to the shorter wavelengths. The recently introduced A$_{60}$
amplitude of the flickering light source in all studied photometric bands is
systematically lower when the negative superhump is gone in season 2021.
