This is actually a tricky case -- 25 years ago the "and I" construction was unequivocally wrong. But things have changed and that usage has become much more common. I not quite willing to say it's fine just yet, but it probably will be in a decade or two
According to my (old-school) brain, there should definitely be a "me" involved, but I keep thinking that it's "me and Bob". The more I look at it, though, the less confident I become. Me hates it when that happens.