The main difference is that with 'बात करना', it's usually a two-way conversation while with बोलना, it's one-way speech. In addition, बोलना may also be used as 'to say'. When you're discussing something with your boss or chatting with your friend, use 'बात करना'. With a parrot saying something, a speaker giving a TED talk or when you're telling your mom about your last vacation while she is just listening, use बोलना.
In addition, you also have the words बताना and कहना that are similar to 'to tell' and 'to say' respectively.