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The origin of sub-TeV gamma rays detected by the \textit{Fermi}-Large AreaTelescope (LAT) from the \textit{Fermi} Bubbles (FBs) at the Galactic center isstill uncertain. In a hadronic model, acceleration of protons and/or nuclei andtheir subsequent interactions with gas in the bubble volume can produce theobserved gamma rays. Recently the High Altitude Water Cherenkov (HAWC)observatory reported an absence of gamma-ray excess from the Northern FB at$b\gtrsim 6^\circ$ Galactic latitude, which resulted in flux upper limits inthe energy range of $1.2-126$ TeV. These upper limits are consistent with thegamma-ray spectrum measured by \textit{Fermi}-LAT at $|b|\ge 10^\circ$, wherean exponential cutoff at energies $\gtrsim 100$ GeV is evident. However, the FBgamma-ray spectrum at $|b|\le 10^\circ$, without showing any sign of cutoff upto around 1 TeV in the latest results, remains unconstrained. The upcomingCherenkov Telescope Array (CTA) will perform a Galactic center survey withunprecedented sensitivity in the energy between 20 GeV and 300 TeV. In thiswork, we perform both morphological and classic on/off analyses with plannedCTA deep central and extended survey and estimate the sensitivity of CTA to theFB hadronic gamma-ray flux models that best fit the spectrum at $|b|\le10^\circ$ and whose counterpart neutrino flux model best fits the optimisticneutrino spectrum from IceCube Neutrino Observatory. We also performsensitivity analysis with a future ground-based Cherenkov detector the LargeHigh Altitude Air Shower Observatory (LHAASO). We find that CTA will be able todiscover or constrain the FB gamma-ray flux at $|b|\le 10^\circ$ in the$\approx$ 200 GeV -- 100 TeV range with planned observation strategy, whileLHAASO may constrain emission in the $\approx 100$~GeV -- 100~TeV range if$\lesssim 10\%$ systematic uncertainties can be achieved.

Constraints on very high energy gamma-ray emission from the Fermi Bubbles with future ground-based experiments