I always teach my flute players thumb Bflat and have them keep their finger on the B flat side. By the time we introduce B natural or high F sharp they are much more familiar with the instrument and it is not a big deal to learn how and when to place your thumb on the natural side. At the end of the 6th grade year we learn what situations warrant the natural side. More often than not its on the flat side.

I also teach lever B flat in addition to 1 and 1 B flat but I am a weirdo I think