  We investigate the nonequilibrium energetics near a critical point of a
non-linear driven oscillator immersed in an active bacterial bath. At the
critical point, we reveal a scaling exponent of the average power
$\langle\dot{W}\rangle\sim (D_{\rm a}/\tau)^{1/4}$ where $D_{\rm a}$ is the
effective diffusivity and $\tau$ the correlation time of the bacterial bath
described by a Gaussian colored noise. Other features that we investigate are
the average stationary power and the variance of the work both below and above
the saddle-node bifurcation. Above the bifurcation, the average power attains
an optimal, minimum value for finite $\tau$ that is below its zero-temperature
limit. Furthermore, we reveal a finite-time uncertainty relation for active
matter which leads to values of the Fano factor of the work that can be below
$2k_{\rm B}T_{\rm eff}$, with $T_{\rm eff}$ the effective temperature of the
oscillator in the bacterial bath. We analyze different Markovian approximations
to describe the nonequilibrium stationary state of the system. Finally, we
illustrate our results in the experimental context by considering the example
of driven colloidal particles in periodic optical potentials within an E. Coli
bacterial bath.
