>>File names with spaces are generally a PITA in CMD files. If there's a chance you could get the file named something like "Detail_with_Text_Report.BAI2" that would be easier to handle. Nevertheless the following should work:
>>

>>copy %srce%*.bai* %trgt%
>>

>
>Аhem...
>
>

>copy "%srce%*.bai* "%trgt%"
>

I tested interactively before I posted. I had a folder with some .txt files that started with the letter "c", some of which included spaces in the file name. I ran

copy c*.txt {destination folder}

All the files, including the ones with spaces, copied as expected.

I also thought about wrapping with double quotes, dunno how that would affect things. I think you missed one in your post, anyways ;)

Just this afternoon I ran into a case where double quotes were needed. If you're willing to put plaintext credentials in a CMD file you can automate drive mapping to remote machines not on the same domain e.g.

NET USE F: \\SomeServer\SomeShare MyPassword /USER:SomeDomain\SomeUserAccount /persistent:y

This afternoon it turned out the password ended in "?". The NET USE command kept throwing errors about bad account name or password. After I wrapped the password in double quotes, all was well.