According to this Guardian article, about the book “P is for Pterodactyl: The Worst Alphabet Book Ever”, there is one word in the English language which starts with a silent B. Unfortunately, they don’t tell us which word it is, and I’d quite like to know!
The word is ”Bdellium” pronounced /ˈdɛliəm/. It is a semi-transparent resin, extracted from trees in Africa. It is used as an incense, and is sometimes passed off as myrrh, due to the price difference.
It is sometimes spelt “Bdellion”, and comes from the Greek “βδέλλιον.”