There are plenty of Bluetooth modules with UART connections, but of
course you need something at the other end. A couple of Silicon Labs
evaluation boards can be configured as linked to each other - then they
can act mostly like a UART cable with a wireless cable, with very little
effort.
If you need to have the Bluetooth module inside the device, and have one
master PC talking to lots of devices, then you'll need to do a bit more
work. And if it is always installed, then suddenly your device is
classified as a radio communications device, with all the standards,
certifications, EMC rules, and testing that goes along with that.
If it is okay to plug something temporarily into the board that needs
debugged, you could set up a Rasberry Pi with a USB battery pack, and
plug that into your TTL-level UART debug signals on the board. Then you
can have Wifi configured in any way you like. A tty to tcp/ip port
converter for remote access should not be difficult to make - with
Python Twisted, it's probably no more than a couple of dozen lines.