This paper provides a generic way to fabricate a high-index contrast tapered waveguide platform based on dielectric crystal bonded on glass for sensing applications. As a specific example, KLu(WO4)2 crystal on a glass platform is made by means of a three-technique combination. The methodology used is on-chip bonding, taper cutting with an ultra-precise dicing saw machine and inductively coupled plasma-reactive ion etching (ICP-RIE) as a post-processing step. The high quality tapered waveguides obtained show low surface roughness (25 nm at the top of the taper region), exhibiting propagation losses estimated to be about 3 dB/cm at 3.5 m wavelength. A proof-of-concept with crystal-on-glass tapered waveguides was realized and used for chemical sensing.