There's increasingly adoption of this unit [bits] everywhere from what I've been seeing.
Yesterday you could get 2200 bits for a dollar, today you can only get 2050 bits.
My hardware vendor says you can get a lot more bits for one dollar. The word is already taken.
Wikipedia says that it was used for money before your hardware vendor was born: http://en.wikipedia.org/wiki/Bit_(money)
The word "bit" has several meanings, as do many words. These are examples of homonyms. Humans are quick to interpret the correct definition from the context in which the word was used.
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I agree with Danny, I will stick with what people actually use and where I live, I never heard "bit" for bitcoin.
It is important for communication for words to have consistent meaning, so, like you said, it would make sense to use words that your audience understands. Language naturally evolves so that words used frequently tend to be short and simple and words used less frequently tend to be longer and more complex. I believe our language will evolve to use "bits," and only time will tell.