A method of bonding a nanofiber web of nanofibers having diameters of between about 50 nanometers and about 2,000 nanometers onto a surface of a woven or nonwoven polymeric media having media fiber diameters of between about 700 nanometers and about 50,000 nanometers utilizes exposing the topmost layer of nanofibers and media fibers to a jet of heated air for a time and at a distance such that substantially only the topmost layer of fibers are bonded. The jet of heated air exits through a nozzle slot having a length of less than about 2 inches in the nanofiber web travel direction. The temperature of the heated air ranges from about 2 to about 10 times the nanofiber melting temperature, and heat air has a nozzle slot velocity of greater than about 500 feet/minute. An adhesive may bond the nanofibers, to a media, which may be bi-component fiber fibers.