We report experimental and theoretical evidence for the formation of chiral bobbers - an interfacial topological spin texture - in FeGe films grown by molecular beam epitaxy (MBE). After establishing the presence of skyrmions in FeGe/Si(111) thin film samples through Lorentz transmission electron microscopy and topological Hall effect, we perform magnetization measurements that reveal an inverse relationship between film thickness and the slope of the susceptibility (dc{hi}/dH). We present evidence for the evolution as a function of film thickness, L, from a skyrmion phase for L < LD/2 to a cone phase with chiral bobbers at the interface for L > LD/2, where LD ~ 70 nm is the FeGe pitch length. We show using micromagnetic simulations that chiral bobbers, earlier predicted to be metastable, are in fact the stable ground state in the presence of an additional interfacial Rashba Dzyaloshinskii-Moriya interaction (DMI).