On PC-compatible systems, the phantom drive "B:" is not provided by the BIOS, but by DOS. The intention of the phantom drive is that you can copy files from one floppy to a different floppy using "copy a:file.txt b:". DOS keeps record of whether the drive was accessed last using the letter "A:" or "B:", and when you access the other letter, DOS outputs the message "Please insert disk in drive X: and press enter to continue".
The easiest way to determine the number of floppy drives on AT-compatible computers is calling INT 13, AH=08. If a drive is present, you will get the type, if the drive is missing, you get the carry flag set. AH=08 is supported for hard drives since the XT (by the hard drive controller BIOS), but floppy drive support for AH=08 only appeared with the AT (in the mainboard BIOS). Another common way to determine the number of floppy drive (starting at the AT) is just checking the CMOS byte containing the drive types. The only PC compatible method is INT11, though, so I expect DOS to call INT11.