That broken male threaded fitting is in fact the choke stove heat tube port that feeds hot air from your exhaust to the automatic choke mechanism hiding inside that round dial shaped housing with the black plastic adjuster disc.
The heat tube would have had the other end attached to a sheetmetal shield surrounding a horizontal leg of the exhaust manifold forward of the carb location. It fed hot air as the engine warmed up to actuate the automatic choke as your engine warmed up. Perhaps you can take more pictures of the engine manifolds to see what is there. It is possible that the BC carb you have may not be the original carb for the bus. It could be a transplant and your engine may have had a manual choke instead of an auto choke, but we need more pics to try and figure that out.
Note - Without the heat tube your automatic choke won't function normally. It may be that its adjusted to keep the choke off all the time, which woud lead to poor starting and warm up operation, but once it's warmed up would run mostly okay.
Without knowing more details on the specific BC carb you have, I can't help on the internal vent tube. You should look at the carb closely as there are some casting numbers on the main bowl and throttle base that may help ID it, guessing that the original carb ID tag is missing.
I thought it might be the hot air but I was looking through the service manual in the tech tips and Figure 7 Choke System has the other tube listed as the Hot Air Tube and shows the connection to the manifold on the same side. Reading further though it tells me that is the choke suction tube which I thought originally. If it is just the hot air connection I think there is enough threads on it that I can make a connection and use that kit Hotrod Lincoln linked. (Ha. Lincoln linked. Mind of a child I have)
There was a casting number and I thought I got a picture when I had it apart but apparently the phone decided that one didn't take. I think it was on the bottom of the bowl. I'll have a look. I'll have to pull the carb anyway once I get some new throttle plate screws. One was missing. 😬
