On second thought, would "ih" be a better choice for the "i" in bit? Perhaps not; I wish I had the IPA keyboard overlay.
That /capital i/ character is unique and would be a perfect application here, which can always be tweaked by diacritic marks.
When I was teaching ESL, I had one Russian and several Greek students, who have both the /i/ and that capital i sound in their language, but when I presented them with the word sheet, it came out profane because they substituted the /i/ in sheet for the /capital i/. They had overcorrected!
Instead of saying "Look at the beautiful sheets" when they were at JC Penneys, what came out of their mouths caused the salesperson to stand there with an open mouth.
