When using pronouns as subjects and d.o.s, is it Bob and I went......... or is
it Bob and me went.....?
Pronouns 'I' and 'we' have been confusing non-native English speakers for a long time and they still continue do so. One easy way to crack the delimma is to cut some of the unnecessary parts of the sentence and see if the pronoun used is correct or not. For example, if we cut the words 'Bob' and 'and' from your example, we are left with 'me.' Can we say "Me went to the park"? I don't think so. What can we say, then? "Bob and I went to the park."
Another example: The man spoke to Ali and I. Here if we cut 'Ali' and 'and', we are left with only the pronoun 'I', which, in this sentence, functions as an object but is certainly not in the objective case. So we can infer that the sentence is wrong. The correct sentence would be, "The man spoke to Ali and me."