In several places online, the 7-branched, golden menorah that stood in the Mishkan/Temple is said to represent the “burning bush” at which Mosheh first stands before G-d.
This lovely interpretation has no apparent basis in traditional Jewish or Christian teachings, although I did come across the following (which I liked):
“In Eastern [Christian] Orthodoxy a tradition exists, originating in the Orthodox Fathers of the Church and its Ecumenical Synods (or Councils), that the flame Moses saw was in fact God’s Uncreated Energies/Glory, manifested as light, thus explaining why the bush was not consumed. Hence, it is not interpreted as a miracle in the sense of an event, which only temporarily exists, but is instead viewed as Moses being permitted to see these Uncreated Energies/Glory, which are considered to be eternal things; the Orthodox definition of salvation is this vision of the Uncreated Energies/Glory…” 
The absence of a traditional citation doesn’t invalidate interpreting “menorah” as “burning bush,” especially for teaching purposes, but it’s a good example of how one post about it — on Wickipedia, for example — can be uncritically quoted as “fact” by many subsequent writers and interpreters.
To interpret the menorah in this way might fall more within the province of “midrash” — in which a verse of Torah is simply the starting point for an almost jazz-like, “improvisational” homily, meant to teach a spiritual lesson rather than serve as a literal interpretation.
It can make excellent, inspiring sermons and essays. But was the menorah literally intended to represent or recall Mosheh’s vision at the “burning bush?”
I’d say “No” for the following reasons:
Generally, Torah prescribes things as reminders of historical events; for example, “Pesach” (for the exit from Egypt) or “Sukkot” (for living in huts during 40 years in the wilderness). To this extent, an association with the “burning bush” would seem possible.
But the events that Torah refers to usually happened to the entire Israelite community as it came out of Egypt; not just to one person.
The two tablets of the 10-commandments, around which the entire Mishkan/ Temple is structured, were a revelation to the entire community, even though communicated to them by Mosheh alone. The jar of manna, Aaron’s staff, and the brass serpent — all of which were later placed in the Holy of Holies (inner room of the Mishkan/Temple) — were likewise reminders of events that occurred to the entire community. The vision of the “burning bush” happened only to Mosheh.
To be consistent, any interpretation of the menorah would also have to explain the other two objects that stood in the heichal (outer room of the Mishkan/ Temple) with it: the golden incense altar and the golden bread-table. The “burning bush” happened only to Mosheh. If the menorah recalls that, to what events in his life could the other two objects be referring? Although midrashim might be created about this, the plain text of Torah doesn’t seem to make explicit any such connections.
It seems to me (again, creating my own “midrash”) that the three objects — menorah, incense altar and bread-table — taken together, are a reminder of Torah’s description of Creation and perfect life in Eden:
The menorah recalls the seven days of creation; the daily renewal of the lamp a reminder that this process of Creation, beginning with “Light,” is ongoing. The bread on the bread-table is a reminder of G-d sustaining life; the continuous replacement of the bread is an appropriately continuous reminder of this perpetual Divine activity. The fragrance of the incense from the altar recalls the fragrance of blooming, living flowers — especially those in Eden.
“Remembering” doesn’t mean here thinking of an event that’s no longer happening, or even of its “meaning.” Much the opposite; it’s contemplative remembering or re-enactment. What was revealed at Sinai is that G-d is “here” in an endless “now;” as present with us today as when giving Torah; as in Eden; as on the first day of Creation. The ritual and the associated objects reenact the event now.
It’s also important to note that the menorah and other objects, although known to some, perhaps all of the Israelites, were actually only viewed by the Kohanim (and, at times, by the Levi’im). That they were meant to suggest themes for remembering/contemplation certainly seems true. But most of all, it was the Kohanim who were to “contemplate,” to “reenter Eden,” as it were, in order to re-experience the Divine Presence just as Adam and Eve had before their error.
The spiritual revelation of the Kohanim was then to enlighten the Israelites, who are themselves (ourselves) ultimately meant to enlighten the world.
All of this, of course, is also present in the design of the synagogue, based as it is on the Mishkan/Temple. There, we are meant to become like Kohanim: rediscovering ourselves standing in G-d’s Presence, as Mosheh did at Sinai; returning the world to its status as Eden once again.