You have just discovered a difference between a morpheme and phoneme! :-)

Korean ㅂ is a single morpheme (smallest unit of meaning) that can be realized as multiple phonemes (smallest unit of linguistically meaningful sound), here /p/ in a word initial or syllable final position or /b/ in other syllable initial positions, but the end of /p/ for the final ㅂ is not clearly indicated (applosive). Korean speakers mix them all the way without realizing that, just like other languages.

English distinguishes /b/ and /p/ as different morphemes instead, so it's natural that an English approximation uses different characters for them.

Well 김밥 is a weird word in Korea even amoung Koreans. Gim bob is closer to how I hear people from Daejeon or Daegu say it. In Seoul it's closer to Gimbap, and those who also speak English usually pronounce it Kimbap but I'm not sure if that's for my sake or how they actually say it.