If I am not mistaken, the Hebrew word for "in the beginning" in Bereishit 1:1, could have been reishit. However, the word used was bereshit. It is my understanding that the use of bereshit (reishit with a bet at its beginning) is significant in that, by the inclusion of the second letter in the Aleph Bet, may indicate a second beginning, or a recreation. Is my understanding correct?
The b- means "in". Just as in English, where you can't say "the beginning, such-and-such happened" but rather say "in the beginning, such-and-such happened", in Hebrew you need to say b'reshis not reshis. That's why the b- is there.
At least on a basic level, there is no reason why the addition of a bet would signify a second beginning. Furthermore, reishit in Biblical Hebrew cannot mean "in the beginning"; it is an adjective meaning "the first of", and it must be attached to a noun (e.g. "reishit bikkurei admat'cha" - "the first of the fruits of your land").