Both are grammatically correct and in common use. There is nothing about the Present Perfect Continuous tense to requires it to end with "since...". It would be fine to write simply "She has been working." without any extra clause.
The choice of tense depends on what exactly you want to say.
If she has been working in a bank for five years, then she started at least five years ago and has continued until now and she continues to work. This is a little redundant in this example because you have already said the she currently works in a bank.
If she has worked in a bank for five years, that could have been any five years in the past. Maybe she worked for four years a decade ago and has come back to work for the last year.
I have been being here is not idiomatic.
You have probably learned that there is a category of verbs which are only very rarely used in with the progressive/continuous construction: stative verbs like be, know, live, see which express a state rather than an action or event. These verbs have the fundamental sense of a continuing state (which is what the progressive/continuous construction expresses) built into their meanings, so the progressive/continuous is superfluous.
For the same reason these verbs are rarely used with the progressive/continuous perfect construction. Indeed, there is even stronger pressure to avoid the progressive/continuous perfect, because the perfect is also inherently stative: it designates a state which came into being as a result of a prior action or event.
Saying I have been being here for ten years thus adds nothing to the sense of I have been being here for ten years, so we don't say it.
Furthermore: These "rules", like most "rules" of grammar, are not absolute: there are exceptions. But lexical be (that is, be as a main verb, not a component of the progressive or passive construction) is exceptionally resistant to exception, because it is the most "stative" of verbs: it ordinarily expresses nothing beyond a particular state. In consequence, when lexical be is cast in the progressive construction it usually has a different meaning, approximately "temporarily behave":
"John is being a jerk" does not mean that John is a jerk but that John is behaving like a jerk right now.
Best Answer
To my American ear, in your examples, there is absolutely no difference between the two forms, which, in fact, give the same information. This is possible with the verb "live" because it's a dynamic verb that lends itself to either a continuous or a perfect interpretation. This would be true of any such verb which designates ongoing action, as opposed to resultative verbs, where the perfect would express the result or completion of the action:
In the southern states, you sometimes hear "know" used like this in reference to people:
With resultative verbs, there would be two different interpretations: