  Magnetic-field-induced phase transitions are investigated in the frustrated
gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and
calorimetric measurements on single-crystal samples. It is clarified that the
previously reported dielectric anomaly at 8~K in powder samples is not due to a
chiral spin liquid state as has been suggested, but rather to a tiny amount of
a ferroelectric impurity phase. Two field-induced quantum phase transitions
between paraelectric and paramagnetic and ferroelectric and magnetically
ordered states are clearly observed. It is shown that the electric polarization
is a secondary order parameter at the lower-field (gap closure) quantum
critical point but a primary one at the saturation transition. Having clearly
identified the magnetic Bose-Einstein condensation (BEC) nature of the latter,
we use the dielectric channel to directly measure the critical divergence of
BEC susceptibility. The observed power-law behavior is in very good agreement
with theoretical expectations for three-dimensional BEC. Finally, dielectric
data reveal magnetic presaturation phases in this compound that may feature
exotic order with unconventional broken symmetries.
