The design of Whispering Gallery Mode Resonators (WGMRs) used as an optical transducer for biosensing represents the first and crucial step towards the optimization of the final device performance in terms of sensitivity and Limit of Detection (LoD). Here, we propose an analytical method for the design of an optical microbubble resonator (OMBR)-based biosensor. In order to enhance the OMBR sensing performance, we consider a polymeric layer of high refractive index as an inner coating for the OMBR. The effect of this layer and other optical/geometrical parameters on the mode field distribution, sensitivity and LoD of the OMBR is assessed and discussed, both for transverse electric (TE) and transverse magnetic (TM) polarization. The obtained results do provide physical insights for the development of OMBR-based biosensor.