He studied law in Paris and Orléans with little profit, but his contacts with the Greek Hermonymos and with Lascaris opened up a broader sphere of cultural interests for him, and he devoted himself with love to classical antiquity, especially Greek. He held various positions at court (secretary to Louis XII, ambassador to Rome for the coronation of Pope Julius II and to Pope Leo X, travel companion to Francis I, etc.) and was in contact with the most illustrious scholars of his time (besides Lascaris: T. More, Erasmus of Rotterdam, P. Bembo, N. Bérauld, G. Sadoleto, Rabelais, etc.). In 1530 he obtained from Francis I the foundation of the Collegium trilingue (Hebrew, Greek and Latin), which later became the Collège de France; he also founded the Library of Fontainebleau, which was later transferred to Paris and formed the first nucleus of the National Library. Today, the Association G. B. is named after him, under whose auspices, among other things, one of the richest and most valuable collections of Greek and Latin texts is published, known, from the name of the publishing house, as the collana Les Belles Lettres.
Between 1502 and 1505 he published the Latin translation of several treatises by Plutarch, an author much favoured by the humanists. Dating to 1508 are his Adnotationes in XXIV libros Pandectarum, published in Paris in a large folio volume, which, by introducing historical and philological considerations for the first time into the study of Roman law, opened up new avenues for this type of research and in a certain way anticipated Cujas. Six years later, B. inaugurated the study of metrology with the fundamental Libri V de Asse et partibus eius (folio, Paris 1514; reprinted in greatly improved form in Venice in 1522; Italian translation by Gualandi, Florence 1562; a summary, prepared by B. himself at the request of Francis I, was published in Paris in 1522 under the title Summaire ou Epitome du livre de Asse). After a philosophical-moral treatise, in which the author reveals a religious spirit based on feeling rather than on theological speculation (De contemptu rerum fortuitarum libri tres, Paris 1521-26), B. still appears as one of the best humanists and Hellenists with his De studio litterarum recte et commode instituendo (ibid. 1527); with the Commentarii linguae graecae (folio, ibid. 1529; 2nd improved edition posthumous, ibid. 1548), a very rich collection of lexicography, which has been widely drawn upon by all later authors of Greek lexica; with the De philologia (ibid. 1530), an interesting treatise in dialogue form (one chapter was translated into French by L. Le Roy, at the request of Charles IX, in 1572, and published in Paris in 1861 under the title Traité de la vénerie). The passion of the philologist and the zeal of the Christian inspired the pages of De transitu Hellenismi ad Christianismum libri tres (Paris 1534), in which B. expounds the principle that pagan culture does not exclude or stifle faith, but rather elevates man to II. There also survives a collection of Epistolae (ibid. 1520-31), which, however, comprises only a small part (160 letters) of his copious correspondence, and a posthumous work, De l'institution du prince (folio, ibid. 1547), which is a reworking of his Recueil d'apophthegmes, offered to Francis I, a manuscript in the Arsenal Library in Paris (ms. 5103). The Opera omnia was published in 4 large folio volumes in Basel in 1557.
His conciliatory attitude towards the Reformation, the fact that in his will he refused any funeral honours, and the conversion of his widow, Roberta Le Lyeur, to Lutheranism nine years after his death, have led some to think that B. adhered to Protestantism in the last years of his life (E. Haag devotes an entry to him in the dictionary of French Protestants, La France protestante, III, Paris 1852, pp. 74 ff.). But apart from his reproof of the corrupt morals of the clergy, there is no other evidence to support this hypothesis, which is refuted in the biography written by a descendant of his (E. de Budé, Vie de G. B., fondateur du Collège de France, Paris 1884).