> My understanding is that even though Air France and British Airways were charging twice the price of normal first class for Concord, they were losing money on them.

They weren't, the Concordes were quite profitable until 9/11 and the following slump in international travel ( due to fear, increased controls and inconveniences) and increase in oil prices.

> I'm surprised there aren't supersonic business jet though

There are companies trying to build supersonic business jets, like Boom.