We present radial trends of metallicity ([Fe/H]) and abundance ratios ([X/Fe]) for several chemical elements─including C, N, Na, and the so-called α-elements (O, Mg, Si, Ca, and Ti)─in the bulge of M31, out to a projected galactocentric distance of ∼0.6 kpc. We estimated abundances using multiple approaches, including full-spectrum fitting, full-index fitting, and line-strength analysis, in combination with different stellar population models. We first tested these techniques on mock spectra and SDSS stacked spectra of early-type galaxies (ETGs), and then applied them to high-quality long-slit spectroscopy of the M31 bulge obtained with the OSIRIS spectrograph at the Gran Telescopio CANARIAS. We find that O, N, and Na are significantly enhanced relative to Fe across the bulge, with typical abundances ≳0.3 dex. In particular, N and Na show steep central enhancements, reaching ∼0.5 dex. C, Mg, and Si exhibit intermediate enhancements of [X/Fe] ∼ 0.2 dex, with C and Mg decreasing toward the center to ≲0.1 dex; while Ca, and to a lesser extent Ti, closely follow Fe, with [X/Fe] < 0.1 dex within uncertainties. Applying the same analysis to SDSS stacked spectra of ETGs as a function of velocity dispersion revealed that the abundance pattern of the M31 bulge closely resembles that of the most massive galaxies, except for N, which is significantly more enhanced (by ∼0.1 dex) in the bulge. For the bulk of the bulge, chemical evolution models assuming high star-formation efficiency and a short gas infall timescale reproduce the overall trends in [Fe/H] and [X/Fe]. In the central region (≲100 pc), the high metallicity content of the bulge can be explained by either an Initial Mass Function flatter than Salpeter at high mass, or a prolonged star formation. Additional processes, such as differential galactic winds, appear necessary to account for the observed decoupling among α elements and the strong central N enhancement. Our results support a scenario whereby the bulk of the M31 bulge formed during a fast and intense episode of star formation.