Drug delivery science is always an important topic as it studies the delivery of therapeutic payloads to the desired target cells without affecting the healthy tissues/cells, thus minimizing drug-induced toxicity. Aiming towards the targeted drug delivery, the present project deals with the delivery of a polarity-sensitive solvatochromic model drug, namely, salt of 8-anilinonaphthalene-1-sulphonic acid (ANSA) to the model bio-membrane (which mimic several aspects of the real cell membrane), more precisely at the lipid-water interface of L–α-Dipalmitoylphosphatidylcholine (DPPC) phospholipid. The drug delivery process has been activated through the binding of dye with cyclodextrin, acting as a drug transporter. Detailed steady-state and time-resolved spectroscopic studies including molecular docking analysis imply the targeted drug delivery of dye, ANSA, towards the lipid-water interface region of lipid bilayers through encapsulation within the cyclodextrin void. Stronger binding interaction of the dye with the lipid bilayers relative to β-cyclodextrin (β-CD) is the foremost reason for the targeted delivery. The present biophysical interaction studies of drug-lipid interaction, thus, may provide a cordial approach for drug formulation and drug delivery.