I'm also an American and get consistently 80-90% British. It seems to think I pronounce "Bob" in an especially British way. I pronounce it in a way that sounds like "Bahb" to me, same sound as in not and cot (I don't have the cot-caught merger). I believe it's the vowel <ä> in IPA that I use. To my ears that's not the way most UK speakers would pronounce it, which I think is more <ɔ> or <ɒ> for all of Bob/not/cot.