We generalize the semi-analytical line transfer (SALT) model recently introduced by Scarlata and Panagia (2015) for modeling galactic outflows, to account for bi-conical geometries of various opening angles and orientations with respect to the line-of- sight to the observer, as well as generalized velocity fields. We model the absorption and emission component of the line profile resulting from resonant absorption in the bi-conical outflow. We show how the outflow geometry impacts the resulting line profile. We use simulated spectra with different geometries and velocity fields to study how well the outflow parameters can be recovered. We find that geometrical parameters (including the opening angle and the orientation) are always well recov- ered. The density and velocity field parameters are reliably recovered when both an absorption and an emission component are visible in the spectra. This condition implies that the velocity and density fields for narrow cones oriented perpendicular to the line of sight will remain unconstrained. To conclude, we fit the model to 10 highly compact galaxies (commonly referred to as Green Peas). We observe strong evidence for bi-conical geometries.