I'm citing two contrasting answers:
1 - Sforno on Exodus 3:2:1 (using Sefaria.com's translation):
וירא מלאך ה' אליו במראה הנבואה, כי אמנם כאשר יגלו המלאכים בדמות
אנשים בלתי נבואה, כענין לאברהם וללוט ולבלעם ולזולתם, לא יאמר עליהם
וַיֵרָא, אבל יאמר עליהם וַיַרְא, כמו וירא והנה שלשה אנשים, וירא לוט,
וירא את מלאך ה' נצב בדרך:
וירא מלאך ה' אליו, in a prophetic vision. When angels appear to
humans in human garb this is not considered a prophetic vision, i.e.
it is something of a lower order of Divine manifestation. Divine
communications to Avraham, Lot, Bileam, and others like them are not
described as וירא, vayeyrah, “it appeared.” However, the recipient is
described as וירא (vayar), “he saw,” i.e. he is described only in
his active role, not his role as receptacle of G’d’s communication.
Examples of the latter kind of communication occur in Genesis 18,2 as
well as in Genesis 19,1 and in Numbers 22,31.
So, essentially, this explanation would state that this was not a physical bush but a vision, only.
2 - Wikipedia states:
Christian hermits originally gathered at Mount Serbal, believing it to
be the biblical Mount Sinai. However, in the 4th century, under the
Byzantine Empire, the monastery built there was abandoned in favour of
the newer belief that Mount Saint Catherine was the Biblical Mount
Sinai; a new monastery - Saint Catherine's Monastery was built at its
foot, and the alleged site of the biblical burning bush was
identified. The bush growing at the spot (a bramble, scientific name
Rubus sanctus), was later transplanted several yards away to a
courtyard of the monastery, and its original spot was covered by a
chapel dedicated to the Annunciation, with a silver star marking where
the roots of the bush had come out of the ground. The Monks at Saint
Catherine's Monastery, following church tradition, believe that this
bush is, in fact, the original bush seen by Moses, rather than a later
replacement, and anyone entering the chapel is
required to remove their shoes, just as Moses was said to have done so
in the biblical account.
However, in modern times, it is not Mount Saint Catherine, but the
adjacent Jebel Musa (Mount Moses), which is currently identified as
Mount Sinai by popular tradition and guide books; this identification
arose from Bedouin tradition.
Personally, the only credibility I give is to the concept that the bush was located at the spot that was later known as Mt. Sinai. The verse in Exodus 3:1 says that Moses led Jethro's sheep to Horeb, which was later known as Mt. Sinai. Whether Mt. Sinai is the place that is now called St. Catherine or whether at the time when Israel appeared at Mt. Sinai to receive the Torah that same bush was still there, would both be speculative. The Torah mentions nothing about either.