There are a few different answers here, without full context it's hard to say which it is, but as a teenager living in Japan Noah's answer, "Wouldn't that scare anyone?" is what I think is the most likely to be accurate.
In direct translation 「びっくりした」means "I was startled" and 「びっくりするじゃないの?」would be "Isn't it startling?" Which personally I've never heard in the same context, but I'm not a native speaker. Rather than "startled" I wonder if "surprised" would be a better translation? Again depends on the context;-;
Scenarios I can imagine this being said are if person 1 was started and laughed at for being scared, and they want to express that it's only natural that they got scared, "Wouldn't anyone be startled?" But say they startled someone else and they had no reaction, maybe it could be used to say, "Shouldn't you be startled?"
But say for instance two people are talking about a crazy event that happened, then maybe it could be translated into "Isn't / Wasn't that surprising?" or even a situation where one person was surprised and the other wasn't, then it's the same as the above but rather than scared/startled they were surprised.
In spoken Japanese the tone of voice would also help. All the above is assuming the の has a question connotation, but if it were said with a downward tone and possibly whiny sort of way, it could also mean like "Hey don't startle me like that" Like Noah stated.
It's all very confusing hope this helps give more perspective at least, try comparing it to the context and make your own interpretation.