SSTO on Earth requires about 9400 m/s of ∆v depending on the exact acceleration profile and other factors.
Ascent from Mars' surface to low Mars orbit requires only about 3800 m/s, and from there it's another 2500 m/s to break out of Mars orbit and get on a trajectory to intercept Earth -- a total of 6300 m/s. Allocate another 300 m/s or so for touchdown on Earth, for 6600 m/s total.
With a methane engine like Raptor, delivering exhaust velocity around 3615 m/s, the rocket equation tells us that a mass ratio of about 6.2 is needed to manage that, which is relatively modest. The current numbers SpaceX is claiming give a better than 9:1 ratio with 50 tons of return payload, suggesting closer to 7900 m/s ∆v available. The additional 1300 m/s velocity budget could be used for a faster Earth return trajectory or to reduce reentry speed at Earth intercept or both. It appears the BFS can lift off from Mars, reach orbit, and do a TEI burn on a single tank of propellant with a very large return payload.
With no payload at all, the BFS should deliver about 9500 m/s of ∆v, just enough to do SSTO from Earth.
The vast majority of the difference between ∆v required for Earth and Mars SSTO is due to gravity, not atmosphere. For a rocket of Saturn V or BFR scale, the aerodynamic losses on ascent to LEO are on the order of half of one percent of the total ascent ∆v budget; in ascent from Mars, the loss is practically zero. Low Mars orbit velocity is less than half of LEO velocity: 3360 m/s instead of 7770 m/s, and the remaining difference is the "gravity loss" term.
