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From the Slavic hydronym *bugъ /*buga.

First attested in this form around 1620 (referring to a “bedbug”), from earlier bugge (“beetle”), from Middle English bugge (“scarecrow, hobgoblin”) which is traced alternatively to: * a Celtic root found in Scots bogill (“goblin, bugbear”) and obsolete Welsh bwg (“ghost, hobgoblin”); compare Welsh bwgwl (“threat, fear”) and Middle Irish bocanách (“supernatural being”). * Proto-Germanic *bugja- (“swollen up, thick”), from Proto-Indo-European *bʰew-, *bu- (“to swell”); compare Norwegian bugge (“big man”), dialectal Low German Bögge (“goblin, snot”). * or to a word related to buck and originally referring to a goat-shaped spectre. For the “insect” meaning the assonance with Middle English budde (“beetle”), from Old English budda, from Proto-West Germanic *buʀdō, from Proto-Germanic *buzdô, from the same ultimate source as above, might have played a role. Compare Low German Budde (“louse, grub”), Norwegian budda (“newborn domestic animal”), Icelandic budda (“purse”). More at bud. But ultimately this convergence of meaning doesn't prove a conflation of the two terms; they might have existed in parallel since PIE times with similar meanings, even if unnoticed by literary sources. The term is used to refer to technical errors and problems at least as early as the 19th century, predating the commonly known story of a moth being caught in a computer.