I guess it depends when he gives the alibi. If he gives it while being questioned by the police, then presumably he would have ended up going to trial for the correct burglary - the wording in the post suggests to me that Bob makes the choice not to give the alibi when he confesses to the police.

I'm not sure, but I think that if you admit to a different crime during a trial you are likely to be rearrested because of what you have said. But I can't remember whether I only think this through watching shows like Law and Order UK :)