  We present high-cadence ultraviolet through near-infrared observations of the
Type Ia supernova (SN Ia) 2023bee in NGC~2708 ($D = 32 \pm 3$ Mpc), finding
excess flux in the first days after explosion relative to the expected
power-law rise from an expanding fireball. This deviation from typical behavior
for SNe Ia is particularly obvious in our 10-minute cadence $TESS$ light curve
and $Swift$ UV data. Compared to a few other normal SNe Ia with detected early
excess flux, the excess flux in SN 2023bee is redder in the UV and less
luminous. We present optical spectra of SN 2023bee, including two spectra
during the period where the flux excess is dominant. At this time, the spectra
are similar to those of other SNe Ia but with weaker Si II, C II and Ca II
absorption lines, perhaps because the excess flux creates a stronger continuum.
We compare the data to several theoretical models that have been proposed to
explain the early flux excess in SNe Ia. Interaction with either a nearby
companion star or close-in circumstellar material is expected to produce a
faster evolution than seen in the data. Radioactive material in the outer
layers of the ejecta, either from a double detonation explosion or simply an
explosion with a $^{56}$Ni clump near the surface, can not fully reproduce the
evolution either, likely due to the sensitivity of early UV observable to the
treatment of the outer part of ejecta in simulation. We conclude that no
current model can adequately explain the full set of observations. We find that
a relatively large fraction of nearby, bright SNe Ia with high-cadence
observations have some amount of excess flux within a few days of explosion.
Considering potential asymmetric emission, the physical cause of this excess
flux may be ubiquitous in normal SNe Ia.
