Hello Alastair,
Welcome to the forum and to Band-in-a-Box!
I suspect the two programs are attempting to share resources, audio or memory. Two steps you can take are split the audio driver that is used by each program and change the audio latency setting.
Band-in-a-Box can use one of three available audio drivers: WAS, ASIO or MME. WAS and MME are part of the Windows operating system while ASIO typically is audio device specific and supplied by the audio device manufacturer.
In Band-in-a-Box press Ctrl + E to open the "Preferences" window then click on the "Audio" button to open audio preferences. Make sure Band-in-a-Box and Finale are using different audio drivers.
Audio latency is the time, in milliseconds, it takes for the computer to process audio. The length of time it takes from the time the computer receives audio to the time you hear it.
Raising the audio latency number gives the computer more time to process the audio. What number works best generally is system specific so what works for me likely won't work for you. I would adjust the number higher than it presently is. As long as you're listening the number doesn't matter. The only time it matters is when you're recording audio while also listening to playback of the other tracks.
Description: Band-in-a-Box Audio Settings.
Audio driver in green box.
Audio latency in red box.