I can see how it could be used for "poetic" (?) purposes. Probably, a better way to punctuate it then would be: "Bob. He went to the store". Consider the following example:
"Captain Smith. He led the charge and saved the Queen. Her generals? They just stood there petrified".
So "Bob. He went to the store" sounds to me like: "It was Bob that went to the store", more or less.
Consider the full stop. With the comma, it seems hardly acceptable. (It's only an intuitive assertion from a non-native speaker of English)