  The Fermi bubbles are structures observed in gamma rays at GeV energies,
emanating from the central region of our galaxy and extending up to 8.5 kpc
above and below the galactic plane. While initial studies showed a flat
brightness across the entire structure, more recent work found a brightening at
the base. We perform a template-based search for TeV signals from the northern
Fermi bubble and just from the base of it in data from the High Altitude Water
Cherenkov (HAWC) gamma-ray observatory. We employ a profile likelihood approach
to calculate the significance and flux from the search regions. With no
significant signal from the northern Fermi bubble and its base, we report new
upper limits on the integral flux at 95% confidence level. Our integral flux
upper limits for the northern Fermi bubble are more constraining than the
previous limits reported by HAWC. Moreover, we present, for the first time, TeV
limits pertaining to the base of the bubble which constitutes a more fair
comparison to Fermi Large Area Telescope data points close to this particular
region.
