Emanuela's introduction of bicchiere into the mix drove me straight back to my OED from whence I discovered that bicker, in the drinking vessel context, is a Scots variant of beaker. This led me to my AHD, which told me that beaker is probably from Vulgar Latin bicarium (unattested) via Old Norse bikarr. Ultimately it is possibly from Greek bikos, drinking jar, possibly from Egyptian bik(with a dot under the k), oil vessel. Presumably, this unattested bicarium would be the source of the Italian bicchiere.