What progress has been made in computerized bridge play?
There's a fundamental problem that the rules of bridge are not well-defined for computers. Specifically, the rules require that partnerships communicate their agreements - including implicit agreements arising from experience playing with their partner - to their opponents.  No one has really figured out what it means for a computer to communicate its partnership agreements to other humans or to a different computer program.
(Note that it does happen in human bridge where one partnership explains their agreements to their opponents, there is misunderstanding, and a director or an appeals committee has to sort everything out, so these rules are not perfectly well-defined for humans either.)
This is less of a problem if the computer is playing a human designed bidding (and carding) system, but a machine-learning designed bidding system could quite possibly (in my opinion would very likely) be incomprehensible to humans.