don't use WBFS, it's old and deprecated.
just use FAT32, and if the drive is not detected fast enough, then just use IOS58 like I said. it's what ALL other homebrew are using, and it works fine like that.
if still you have issue, it's because you use a FLASH DRIVE instead of real HDD. FLASH DRIVES ARE NOT SUPPORTED. I can't count how many times we said it on this forum. but yes, wbfs can "semi-fix" the detection problem, but not the write problem.
wii backup manager either 32 or 64 bit? well, there's nothing else. that's basically all the possibilities. so, of course, use either one of the two existing version. there's no 16bit version, or 128 bit version....
if you meant "app version" and not the "bit version", then old is not necessarily bad or corrupting hdds. I'm using an old one without issue. of course, newer is probably better for bug fixes, but not always. newer can mean new introduced bugs too.
edit: I might have understand it now : you meant if he uses 32bit windows to not launches 64bit version? and vice versa?
64bit on 32bit windows wouldn't run, and 32bit should work fine on 64bit windows though.
I'm using v0.3.6 build 48 32bit version on win64 and didn't have problem so far, both on WBFS and FAT32 partition format. but that's only because I don't have to deal with partition bigger than 2TB (or else, you need 64bit version)