1. There is more than one way to measure 'price,' and
2. 'willing to buy' and trades executed are two different things.
If you are measuring the price of bitcoin by looking at the price of the last trade that occurred, then you are right: trades need to happen for you to get price information.
But there is also the order book. In [1], thousands of 'intents to trade'/outstanding orders are displayed but no trades are listed.
When I looked at the page, the highest anyone was willing to buy (in this specific order book at this time) was $4076, and the lowest anyone would sell was $4086.
This is a good indicator of the current consensus on Bitcoin price but isn't actually trade data.
Now, let's say the market gets just a little more bullish on Bitcoin and someone places an order to buy at $4080. Has the price of Bitcoin changed? One could argue yes if you judge price from the order book: from ~$4081 to ~$4083 or so. But no trades have occurred.
So back to the original question: in the absence of trade data, the price of bitcoin can be seen from what everyone decides it is, via an order book.
[1] https://www.bitstamp.net/market/order_book/