Bernays was educated at King's College School, and studied chemistry with C. Remigius Fresenius, and afterwards, with Justus Liebig at Giessen, where he graduated PhD.
His doctoral thesis was probably a paper on limonin, a bitter principle which he discovered in the pips of oranges and lemons (published in Buchner's Repertorium für die Pharmacie and abstracted in Liebig's Annalen, 1841, xl.
Bernays was a genial man and a capable and popular teacher; he took a great interest in social matters generally, and gave over a thousand free public lectures during his lifetime.
Besides the works mentioned above he published a small manual on food in 1876, an essay on The Moderate Use of Alcohol True Temperance, published in the Contemporary Review and reprinted with essays by others in The Alcohol Question, various editions of Notes for Students in Chemistry, and miscellaneous lectures on agricultural chemistry and other subjects.
He also carried out investigations on the atmosphere of Cornish mines and on dangerous trades, and made inventions in water filtration.