To paraphrase Eric Voorhees,
Bitcoin is unfortunately the name of two things.
1) it is the name of the Bitcoin protocol, which describes how the block chain, mining, etc. works.
This protocol performs some useful functions that no other money system can currently match. (Fast cheap transfer to any where in the world, robust etc etc) The Bitcoin protocol clearly has a value, and the value comes from its utility.
2) The Bitcoin protocol has been implemented to allow transfer of a digital currency, this currency is also called Bitcoin. A Bitcoin has no intrinsic value and is commonly misuderstood to be what Bitcoin is all about.
As far as modern economics is concerned there is no such notion as
intrinsic value. It does really exist in finances but it has very specific usage which has nothing do with what is being discussed here. To say that Bitcoin as a currency doesn't have intrinsic value would automatically imply there is something which has such value. This is false