I'm taking lessons on Memrise.com.
Memrise indicates that both can mean, "she's going to a bar":
- Va a un bar
- Se va a un bar
Why the difference in Spanish?
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In the first sentence you provided, Va a un bar, "va" is a conjugated (3rd person singular, present) form of the verb ir and the sentence means "She is going to a bar".
In the second sentence, Se va a un bar, "se va" is a conjugation of irse and the sentence could be translated as "She is leaving for a bar."
It is important to distinguish between ir and irse. At the starting point of the movement they can be somewhat interchangable. For instance, in the examples you shared, if the subject is presently sitting at home, the meanings of each are subtly different. (Choosing "leaving / se va" definitely emphasizes the act of initiating outward movement / exiting, vs "going / va" which is more focused on movement towards a destination.) But say either one in this context and it will basically be understood the same way: she is presently on her way out of the house, headed for the bar.
But things are different if the subject is presently sitting in a car, already en route to the bar. If you said "Va a un bar." somebody would understand what you meant: she is on her way to the bar right now (in the car). But if you said to someone who didn't already know where she was coming from "Se va a un bar." it would would make them wonder where she is leaving from. (Is she leaving home? Work? The car? etc.)