The original word is ビビる, meaning to be nervous or frightened. ビビらす then should mean to make someone nervous or frightened, although it doesn't seem to be a formal word.
Well, it does appear to be a word, as a google search would attest, however, it seems to be extremely uncommon slang. Looking at the google images that it returns (various shocked faces, and things that look a bit ugly/intimidating), and with the knowledge that ビビる is 'to be apprehensive'/'to be afraid of', my educated guess is that it's something of a taunt; 'Are you afraid?'/'Are you having second thoughts?'/'Are you chicken?'. Now, in your example, ビビらすんじゃ, I'd say that the best interpretation is that she's asking 'Are you chicken?'. In longer form, it would be ビビらすのじゃんか？ (Is it that you're afraid?)
That's just my two cents on what appears to be some pretty obscure slang. Hopefully it helps you get an idea of what the sentence means.
cmertb has answered the question already, but I searched the word anyway.
I was surprised to see that the word had been used since Heian Period (794-1192).
Reference Link (in Japanese): 日本語俗語辞典
ビビる is quite a common word, but is generally used more by men. It's not all that a classy word.
【ビビる/being scared】 ビビってんじゃねーよ： Don't be such a chicken. Don't get so scared.
【ビビらす/scare (someone)】ビビらすんじゃねーよ： Don't scare me.
---------- Post added at 11:51 AM ---------- Previous post was at 11:48 AM ----------
ビビってんのか？（Are you being scared?）
何ビビってんだよ？（Why are you so scared?）
子供ビビらしてんじゃねーよ/ビビらすんじゃねーよ（Don't frighten a little kid. ）
Last edited by mikkih; October 09, 2013 at 11:34 AM.