To web-search (two syllables)

To google (two syllables, only slightly glibber, due to no "b-s" plosive-fricative combo).

Maybe "web search" can be shortened to "bsearch" or "besearch", like "web log" got shortened to "blog".

"besearch" has grammatical precedence: bestow, bequeath, behead, bewitch, belabor, befriend, ...