An elliptical accretion disk following the tidal disruption event AT 2020zso

[Abridged] We classify AT 2020zso as a TDE based on the blackbody evolution inferred from UV/optical photometric observations, and spectral line content and evolution. We identify transient, double-peaked Bowen (N III), He I, He II and Halpha emission lines. We model medium resolution optical spectroscopy of the He II (after careful deblending of the N III contribution) and Halpha lines during the rise, peak and early decline of the light curve using relativistic, elliptical accretion disk models. We find that the spectral evolution before peak can be explained by optical depth effects consistent with an outflowing, optically thick Eddington envelope. Around peak the envelope reaches its maximum extent (approximately 10^15 or 3000-6000 gravitational radii for an inferred black hole mass of 5-10 10^5) and becomes optically thin. The Halpha and He II emission lines at and after peak can be reproduced with a highly inclined (i=85+-5 degrees), highly elliptical (e=0.97+-0.01) and relatively compact (Rin = several 100 Rg and Rout = several 1000 Rg ) accretion disk. Overall, the line profiles suggest a highly elliptical geometry for the new accretion flow, consistent with theoretical expectations of newly formed TDE disks. We quantitatively confirm, for the first time, the high inclination nature of a Bowen (and X-ray dim) TDE, consistent with the unification picture of TDEs where the inclination largely determines the observational appearance. Rapid line profile variations rule out the binary SMBH hypothesis as the origin of the eccentricity; these results thus provide a direct link between a TDE in an AGN and the eccentric accretion disk. We illustrate for the first time how optical spectroscopy can be used to constrain the black hole spin, through (the lack of) disk precession signatures (changes in inferred inclination) - and rule out high black hole spin values (a < 0.8).