I call it TBT because the section of the forum where it is primarily used is called the TBT Marketplace. But as KaydeeKrunk said above me, BTB makes more sense.
For years, the currency was just known as TBT. No one cared what it stood for in regards to the currency, but everyone knew it referred to the currency. Yes, it does actually stand for "The Bell Tree", and when people used it they said "TBT Bells", not just TBT.
In the past year or so, some people started using BTB to mean "Bell Tree Bells" and it just caught on. It's widely understood to also mean the currency, but people use both.
When I first joined, I always just used BTB since everyone used it at the time and it was the norm. With the massive wave of new members in 2015/2016, TBT is now more commonly used, so I use TBT instead. BTB makes more sense though, and I'm hoping it becomes the norm to use it again.
Yup, I'm the same way. Ever since I joined the site I've seen it called TBT more often than not so whenever I see it called BTB I think it looks wrong in a way.