The Fed sets the overnight borrowing costs by setting its overnight target rate. The markets determine the rates at which the treasury can borrow through the issuance of bonds.
The Fed's actions will certainly influence the price of very short term bonds, but the Fed's influence on anything other than very short term bonds in the current environment is very muted.
Currently, the most influential factor keeping bond prices high and yields low is the high demand for US treasuries coming from overseas governments and institutions. This is being caused by two factors : sluggish growth in overseas economies and the ongoing strength of the US dollar. With many European government bonds offering negative redemption yields, income investors see US yields as relatively attractive. Those non-US economies which do not have negative bond yields either have near zero yields or large currency risks or both. Political issues such as the survival of the Euro also weigh heavily on market perceptions of the current attractiveness of the US dollar. Italian banks may be about to deliver a shock to the Eurozone, and the Spanish and French banks may not be far behind.
Another factor is the continued threat of deflation. Growth is slowing around the world which negatively effects demand. Commodity prices remain depressed. Low growth and recession outside of the US translate into a prolonged period of near zero interest rates elsewhere together with renewed QE programmes in Europe, Japan, and possibly elsewhere.
This makes the US look relatively attractive and so there is huge demand for US dollars and bonds. Any significant move in US interest rates risks driving to dollar ever higher which would be very negative for the future earning of US companies which rely on exports and foreign income. All of this makes the market believe that the Fed's hands are tied and low bond yields are here for the foreseeable future.
Of course, even in the US growth is relatively slow and vulnerable to a loss of steam following a move in interest rates.