Hello Andrew,
Hello Mac,

thank you very much for your helpful hints!
Here is, what I could find out up to now:
I was wrong in my opinion about the default setting of my keyboards hardware. I forgot that I changed from the default setting to a higher quality setting years before: 96 kHz at 24 bits. (This setting worked fine - before the conductor feature came up; and the sound quality was really fine!)
So I changed that setting to 44.1 kHz at 16 bits now.

But then next problem came up: the computer didn't recognize the keyboard any longer. I had to deinstall the driver software and install it anew.

And the next problem arose: installing the driver failed with this setting. An error report suggested to install the driver with a hardware setup of at least 44.1 kHz and 24 bits.

So this is my dilemma now: My hardware combination of computer and keyboard needs the 44.1/24 setting, but BIAB seems to only work fine with the 44.1/16 setting; at least for the use of the conductor feature.

With the 44.1/24 setting, and reducing the ASIO buffer size I'm able to push down the latency to less than 12 ms, though. With this setting my original problem became smaller. Sometimes the conductor even works without any problems, but I can't rely on that. For using the conductor feature in live performances I have to be sure that it works fine.

But, thanks to your help, I know now that the problem is not (so much) BIAB, but my hardware combination, and, the ASIO settings. I will continue to work on that. Hopefully I'll find a convenient solution. I will let you know then.
Thanks again!

Greetings from germany
Ulrich