We present a novel scheme for dense electron acceleration driven by the laser irradiation of a near-critical-density plasma. The electron reflux effect in a transversely tailored plasma is particularly enhanced in the area of peak density. We observe a bubble-like distribution of re-injected electrons, which forms a strong quasistatic electromagnetic field that can accelerate electrons longitudinally while also preserving the electron transverse emittance. Simulation results demonstrate that over-dense electrons could be trapped in such an artificial bubble and accelerated to an energy of $\sim 500\mathrm{M}\mathrm{e}\mathrm{V}$. The obtained relativistic electron beam can reach a total charge of up to 0.26 nC and is well collimated with a small divergence of 17 mrad. Moreover, the wavelength of electron oscillation is noticeably reduced due to the shaking of the bubble structure in the laser field. As a result, the energy of the produced photons is substantially increased to the γ range. This new regime provides a path to generating high-charge electron beams and high-energy γ-ray sources.