  We study bulge formation in MW/M31-like galaxies in a $\Lambda$-cold dark
matter scenario, focusing on the origin of high- and low-Sersic index bulges.
For this purpose we use TNG50, a simulation of the IllustrisTNG project that
combines a resolution of $\sim 8 \times 10^4 M_{\odot}$ in stellar particles
with a cosmological volume 52 cMpc in extent. We parametrize bulge surface
brightness profiles by the S\'ersic index and the bulge-to-total (B/T) ratio
obtained from two-component photometric decompositions. In our sample of 287
MW/M31-like simulated galaxies, $17.1\%$ of photometric bulges exhibit
high-S\'ersic indices and $82.9\%$ show low-S\'ersic indices. We study the
impact that the environment, mergers and bars have in shaping the surface
brightness profiles. We explore two different definitions for local environment
and find no correlation between bulge properties and the environment where they
reside. Simulated galaxies with higher S\'ersic indices show, on average, a
higher fraction of ex-situ stars in their kinematically selected bulges. For
this bulge population the last significant merger (total mass ratio $m_{\rm
sat}/m_{\rm host} > 0.1$) occurs, on average, at later times. However, a
substantial fraction of low-S\'ersic index bulges also experience a late
significant merger. We find that bars play an important role in the development
of the different types of photometric bulges. We show that the fraction of
simulated galaxies with strong bars is smaller for the high- than for the
low-S\'ersic index population, reaching differences of $20\%$ at $z > 1$.
Simulated galaxies with high fractions of ex-situ stars in the bulge do not
develop strong bars. Conversely, simulated galaxies with long-lived strong bars
have bulges with ex-situ fractions, $f_{\rm ex-situ} < 0.2$.
